{"id":7039,"date":"2021-10-22T15:48:04","date_gmt":"2021-10-22T10:18:04","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7039"},"modified":"2021-11-17T16:14:44","modified_gmt":"2021-11-17T10:44:44","slug":"the-sum-of-first-20-terms-of-the-sequence-0-7-0-77-0-777-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-sum-of-first-20-terms-of-the-sequence-0-7-0-77-0-777-is\/","title":{"rendered":"The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ……. , is"},"content":{"rendered":"

Solution :<\/h2>\n

0.7 + 0.77 + 0.777 + …… + upto 20 terms<\/p>\n

= \\(7\\over 10\\) + \\(77\\over 10^2\\) + \\(777\\over 10^3\\) +\u00a0 ….. + upto 20 terms<\/p>\n

= 7[ \\(1\\over 10\\) +\u00a0 \\(11\\over 10^2\\) + \\(111\\over 10^3\\) +\u00a0 ….. + upto 20 terms ]<\/p>\n

= \\(7\\over 9\\)[ \\(9\\over 10\\) +\u00a0 \\(99\\over 100\\) + \\(999\\over 1000\\) +\u00a0 ….. + upto 20 terms ]<\/p>\n

= \\(7\\over 9\\)[ (1 – \\(1\\over 10\\)) +\u00a0 (1 – \\(1\\over 10^2\\)) + (1 – \\(1\\over 10^3\\)) +\u00a0 ….. + upto 20 terms ]<\/p>\n

= \\(7\\over 9\\){n – (\\(1\\over 10\\) + \\(1\\over 10^2\\) + ….. + \\(1\\over 10^n\\)}<\/p>\n

= \\(7\\over 9\\)[n – \\(1\\over 10\\)\\((1 – ({1\\over 10})^n)\\over (1 – {1\\over 10})\\)]<\/p>\n

= \\(7\\over 9\\){\\(9n –\u00a0 1 + {1\\over 10^n}\\)}<\/p>\n

\n

Similar Questions<\/h3>\n

Let \\(a_n\\) be the nth term of an AP. If \\(\\sum_{r=1}^{100}\\) \\(a_{2r}\\) = \\(\\alpha\\) and \\(\\sum_{r=1}^{100}\\) \\(a_{2r-1}\\) = \\(\\beta\\), then the common difference of the AP is<\/a><\/p>\n

A man saves Rs 200 in each of the first three months of his service. In each of the subsequent months, his saving increases by Rs 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs 11040 after<\/a><\/p>\n

If 100 times the 100th term of an AP with non-zero common difference equal to the 50 times its 50th term, then the 150th term of AP is<\/a><\/p>\n

If x, y and z are in AP and \\(tan^{-1}x\\), \\(tan^{-1}y\\) and \\(tan^{-1}z\\) are also in AP, then<\/a><\/p>\n

Find the sum of n terms of the series 1.3.5 + 3.5.7 + 5.7.9 + \u2026\u2026<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : 0.7 + 0.77 + 0.777 + …… + upto 20 terms = \\(7\\over 10\\) + \\(77\\over 10^2\\) + \\(777\\over 10^3\\) +\u00a0 ….. + upto 20 terms = 7[ \\(1\\over 10\\) +\u00a0 \\(11\\over 10^2\\) + \\(111\\over 10^3\\) +\u00a0 ….. + upto 20 terms ] = \\(7\\over 9\\)[ \\(9\\over 10\\) +\u00a0 \\(99\\over 100\\) + \\(999\\over …<\/p>\n

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ……. , is<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,57],"tags":[],"yoast_head":"\nThe sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ....... , is<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" 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