{"id":8273,"date":"2021-11-20T01:15:44","date_gmt":"2021-11-19T19:45:44","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8273"},"modified":"2021-11-20T01:28:20","modified_gmt":"2021-11-19T19:58:20","slug":"find-the-middle-term-in-the-expansion-of-2over-3x2-3over-2x20","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-middle-term-in-the-expansion-of-2over-3x2-3over-2x20\/","title":{"rendered":"Find the middle term in the expansion of \\(({2\\over 3}x^2 – {3\\over 2x})^{20}\\)."},"content":{"rendered":"

Solution :<\/h2>\n

Here, n = 20, which is an even number.<\/p>\n

So, \\({20\\over 2} + 1\\)th term i.e. 11th term is the middle term<\/a>.<\/p>\n

Hence, the middle term<\/a> = \\(T_{11}\\)<\/p>\n

\\(T_{11}\\) = \\(T_{10 + 1}\\) = \\(^{20}C_{10}\\) \\(({2\\over 3}x^2)^{20 – 10}\\) \\((-{3\\over 2x})^{10}\\)<\/p>\n

= \\(^{20}C_{10} x^{10}\\)<\/p>\n


\n

Similar Questions<\/h3>\n

Find the middle term in the expansion of \\((3x \u2013 {x^3\\over 6})^7\\).<\/a><\/p>\n

Find the 9th term in the expansion of \\(({x\\over a} \u2013 {3a\\over x^2})^{12}\\).<\/a><\/p>\n

Find the 10th term in the binomial expansion of \\((2x^2 + {1\\over x})^{12}\\).<\/a><\/p>\n

Which is larger \\((1.01)^{1000000}\\) or 10,000?<\/a><\/p>\n

By using binomial theorem, expand \\((1 + x + x^2)^3\\).<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Here, n = 20, which is an even number. So, \\({20\\over 2} + 1\\)th term i.e. 11th term is the middle term. Hence, the middle term = \\(T_{11}\\) \\(T_{11}\\) = \\(T_{10 + 1}\\) = \\(^{20}C_{10}\\) \\(({2\\over 3}x^2)^{20 – 10}\\) \\((-{3\\over 2x})^{10}\\) = \\(^{20}C_{10} x^{10}\\) Similar Questions Find the middle term in the expansion …<\/p>\n

Find the middle term in the expansion of \\(({2\\over 3}x^2 – {3\\over 2x})^{20}\\).<\/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":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[177,43],"tags":[],"yoast_head":"\nFind the middle term in the expansion of \\(({2\\over 3}x^2 - {3\\over 2x})^{20}\\).<\/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:\/\/mathemerize.com\/find-the-middle-term-in-the-expansion-of-2over-3x2-3over-2x20\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the middle term in the expansion of \\(({2\\over 3}x^2 - {3\\over 2x})^{20}\\).\" \/>\n<meta property=\"og:description\" content=\"Solution : Here, n = 20, which is an even number. So, ({20over 2} + 1)th term i.e. 11th term is the middle term. Hence, the middle term = (T_{11}) (T_{11}) = (T_{10 + 1}) = (^{20}C_{10}) (({2over 3}x^2)^{20 – 10}) ((-{3over 2x})^{10}) = (^{20}C_{10} x^{10}) Similar Questions Find the middle term in the expansion … Find the middle term in the expansion of (({2over 3}x^2 – {3over 2x})^{20}). 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