{"id":22650,"date":"2021-09-27T09:20:59","date_gmt":"2021-09-27T03:50:59","guid":{"rendered":"https:\/\/python-programs.com\/?p=22650"},"modified":"2021-11-22T18:35:38","modified_gmt":"2021-11-22T13:05:38","slug":"python-program-to-find-sum-of-series-1-22-33-5-n-n1","status":"publish","type":"post","link":"https:\/\/python-programs.com\/python-program-to-find-sum-of-series-1-22-33-5-n-n1\/","title":{"rendered":"Python Program to Find Sum of Series 1\/2!+2\/3!+3\/5!+&#8230;..N\/(N+1)!"},"content":{"rendered":"<p>In the previous article, we have discussed <a href=\"https:\/\/python-programs.com\/python-program-to-find-sum-of-series-5-2-10-2-15-2-n-2\/\">Python Program to Find Sum of Series 5^2+10^2+15^2+&#8230;..N^2<\/a><br \/>\nGiven a number N and the task is to find the sum of series<strong> (1\/2!+2\/3!+3\/5!+&#8230;..N\/(N+1)!)<\/strong> till the given number N in Python.<\/p>\n<p><strong>Examples:<\/strong><\/p>\n<p><strong>Example1:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given Number (Limit) = 6<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The above series sum till the given number N{ 6 } =  0.9998015873015872<\/pre>\n<p><strong>Example2:<\/strong><\/p>\n<p><strong>Input:<\/strong><\/p>\n<pre>Given Number (Limit) = 13<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The above series sum till the given number N{ 13 } =  0.9999999999885293<\/pre>\n<h2>Program to Find Sum of Series 1\/2!+2\/3!+3\/5!+&#8230;..N\/(N+1)!<\/h2>\n<p>Below are the ways to find the sum of series<strong> (1\/2!+2\/3!+3\/5!+&#8230;..N\/(N+1)!)<\/strong> till the given number N in Python:<\/p>\n<ul>\n<li><a href=\"#Using_While_Loop_(Static_Input)\">Using While Loop (Static Input)<\/a><\/li>\n<li><a href=\"#Using_While_loop_(User_Input)\">Using While loop (User Input)<\/a><\/li>\n<\/ul>\n<h3 id=\"Using_While_Loop_(Static_Input)\">Method #1: Using While Loop (Static Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Import math module using the import keyword.<\/li>\n<li>Give the number N (Limit) as static input and store it in a variable.<\/li>\n<li>Take a variable to say <strong>itr<\/strong> and initialize its value to 1.<\/li>\n<li>Take another variable to say <strong>rsltseries_summ<\/strong> and initialize its value to 0.0 (Floating point number).<\/li>\n<li>Loop until the above-declared variable itr value is less than or equal to the given number using the while loop.<\/li>\n<li>Calculate the factorial of itr+1 using the math.factorial() method and store it in another variable.<\/li>\n<li>Calculate the value of itr divided by the above result factorial and convert it into float using the float() function.<\/li>\n<li>Store it in another variable.<\/li>\n<li>Add the above result to the\u00a0<strong>rsltseries_summ <\/strong>and store it in the same variable.<\/li>\n<li>Increment the above itr value by 1.<\/li>\n<li>Print the sum of series till the given number N.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Import math module using the import keyword.\r\nimport math\r\n# Give the number N(limit) as static input and store it in a variable.\r\ngvn_numb = 6\r\n# Take a variable to say itr and initialize its value to 1.\r\nitr = 1\r\n# Take a variable to say rsltseries_summ and initialize its value to 0.0\r\n# (Floating point number)\r\nrsltseries_summ = 0.0\r\n# Loop until the above-declared variable itr value is less than or equal to the\r\n# given number using the while loop.\r\nwhile(itr &lt;= gvn_numb):\r\n    # Calculate the factorial of itr+1 using the math.factorial() method and\r\n    # store it in another variable.\r\n    factrl = math.factorial(itr+1)\r\n    # Calculate the value of itr divided by the above result factorial and convert it\r\n    # into float using the float() function.\r\n    # Store it in another variable.\r\n    p = float(itr\/factrl)\r\n    # Add the above result to the\u00a0rsltseries_summ and store it in the same variable.\r\n    rsltseries_summ += p\r\n    # Increment the above itr value by 1.\r\n    itr += 1\r\n# Print the sum of series till the given number N.\r\nprint(\r\n    \"The above series sum till the given number N{\", gvn_numb, \"} = \", rsltseries_summ)\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre id=\"codeOutputPre\">The above series sum till the given number N{ 6 } =  0.9998015873015872<\/pre>\n<h3 id=\"Using_While_loop_(User_Input)\">Method #2: Using While loop (User Input)<\/h3>\n<p><strong>Approach:<\/strong><\/p>\n<ul>\n<li>Import math module using the import keyword.<\/li>\n<li>Give the number N (Limit) as user input using the int(input()) function and store it in a variable.<\/li>\n<li>Take a variable to say <strong>itr<\/strong> and initialize its value to 1.<\/li>\n<li>Take another variable to say <strong>rsltseries_summ<\/strong> and initialize its value to 0.0 (Floating point number).<\/li>\n<li>Loop until the above-declared variable itr value is less than or equal to the given number using the while loop.<\/li>\n<li>Calculate the factorial of itr+1 using the math.factorial() method and store it in another variable.<\/li>\n<li>Calculate the value of itr divided by the above result factorial and convert it into float using the float() function.<\/li>\n<li>Store it in another variable.<\/li>\n<li>Add the above result to the\u00a0<strong>rsltseries_summ <\/strong>and store it in the same variable.<\/li>\n<li>Increment the above itr value by 1.<\/li>\n<li>Print the sum of series till the given number N.<\/li>\n<li>The Exit of the Program.<\/li>\n<\/ul>\n<p><strong>Below is the implementation:<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"python\"># Import math module using the import keyword.\r\nimport math\r\n# Give the number N (Limit) as user input using the int(input()) function and \r\n# store it in a variable.\r\ngvn_numb = int(input(\"Enter some Random Number = \"))\r\n# Take a variable to say itr and initialize its value to 1.\r\nitr = 1\r\n# Take a variable to say rsltseries_summ and initialize its value to 0.0\r\n# (Floating point number)\r\nrsltseries_summ = 0.0\r\n# Loop until the above-declared variable itr value is less than or equal to the\r\n# given number using the while loop.\r\nwhile(itr &lt;= gvn_numb):\r\n    # Calculate the factorial of itr+1 using the math.factorial() method and\r\n    # store it in another variable.\r\n    factrl = math.factorial(itr+1)\r\n    # Calculate the value of itr divided by the above result factorial and convert it\r\n    # into float using the float() function.\r\n    # Store it in another variable.\r\n    p = float(itr\/factrl)\r\n    # Add the above result to the\u00a0rsltseries_summ and store it in the same variable.\r\n    rsltseries_summ += p\r\n    # Increment the above itr value by 1.\r\n    itr += 1\r\n# Print the sum of series till the given number N.\r\nprint(\r\n    \"The above series sum till the given number N{\", gvn_numb, \"} = \", rsltseries_summ)\r\n\r\n<\/pre>\n<p><strong>Output:<\/strong><\/p>\n<pre>Enter some Random Number = 13\r\nThe above series sum till the given number N{ 13 } = 0.9999999999885293<\/pre>\n<p>If you are learning Python then the <a href=\"https:\/\/python-programs.com\/python-programming-examples-with-output\/\">Python Programming Example<\/a> is for you and gives you a thorough description of concepts for beginners, experienced programmers.<\/p>\n<ul>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-sum-of-series-11-31-51-7-1-n2\/\">Python Program to Find Sum of Series 1+1\/3+1\/5+1\/7+&#8230;..1\/(N+2)<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-sum-of-series-1-2-3-4-5-n\/\">Python Program to Find Sum of Series 1-2+3-4+5&#8230;+N<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-print-triangular-number-series-1-3-6-10-15-n\/\">Python Program to Print Triangular Number series 1 3 6 10 15 &#8230;N<\/a><\/li>\n<li><a href=\"https:\/\/python-programs.com\/python-program-to-find-sum-of-series-5-2-10-2-15-2-n-2\/\">Python Program to Find Sum of Series 5^2+10^2+15^2+&#8230;..N^2<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In the previous article, we have discussed Python Program to Find Sum of Series 5^2+10^2+15^2+&#8230;..N^2 Given a number N and the task is to find the sum of series (1\/2!+2\/3!+3\/5!+&#8230;..N\/(N+1)!) till the given number N in Python. Examples: Example1: Input: Given Number (Limit) = 6 Output: The above series sum till the given number N{ &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/python-programs.com\/python-program-to-find-sum-of-series-1-22-33-5-n-n1\/\"> <span class=\"screen-reader-text\">Python Program to Find Sum of Series 1\/2!+2\/3!+3\/5!+&#8230;..N\/(N+1)!<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":7,"featured_media":22677,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":"","jetpack_publicize_message":"","jetpack_is_tweetstorm":false,"jetpack_publicize_feature_enabled":true},"categories":[5],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v18.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Python Program to Find Sum of Series 1\/2!+2\/3!+3\/5!+.....N\/(N+1)! - Python Programs<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/python-programs.com\/python-program-to-find-sum-of-series-1-22-33-5-n-n1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Python Program to Find Sum of Series 1\/2!+2\/3!+3\/5!+.....N\/(N+1)! - Python Programs\" \/>\n<meta property=\"og:description\" content=\"In the previous article, we have discussed Python Program to Find Sum of Series 5^2+10^2+15^2+&#8230;..N^2 Given a number N and the task is to find the sum of series (1\/2!+2\/3!+3\/5!+&#8230;..N\/(N+1)!) till the given number N in Python. 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Examples: Example1: Input: Given Number (Limit) = 6 Output: The above series sum till the given number N{ &hellip; Python Program to Find Sum of Series 1\/2!+2\/3!+3\/5!+&#8230;..N\/(N+1)! 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