{"id":8265,"date":"2021-11-20T00:46:12","date_gmt":"2021-11-19T19:16:12","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8265"},"modified":"2021-11-20T01:28:54","modified_gmt":"2021-11-19T19:58:54","slug":"which-is-larger-1-011000000-or-10000","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/which-is-larger-1-011000000-or-10000\/","title":{"rendered":"Which is larger \\((1.01)^{1000000}\\) or 10,000?"},"content":{"rendered":"

Solution :<\/h2>\n

We have, \\((1.01)^{1000000}\\)\u00a0 – 10000<\/p>\n

= \\((1 + 0.01)^{1000000}\\) – 10000<\/p>\n

By using binomial theorem,<\/p>\n

= \\(^{1000000}C_0\\) + \\(^{1000000}C_1 (0.01)\\)\u00a0 + \\(^{1000000}C_2 (0.01)^2\\)\u00a0 + …… + \\(^{1000000}C_{1000000} (0.01)^{1000000}\\) – 10000<\/p>\n

= (1 + 1000000(0.01) + other positive terms) – 10000<\/p>\n

= (1 + 10000 + other positive terms) – 10000<\/p>\n

= 1 + other positive terms > 0<\/p>\n

Hence,\u00a0 \\((1.01)^{1000000}\\) is greater than 10000.<\/p>\n

\n

Similar Questions<\/h3>\n

Find the middle term in the expansion of \\(({2\\over 3}x^2 \u2013 {3\\over 2x})^{20}\\).<\/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

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

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

Solution : We have, \\((1.01)^{1000000}\\)\u00a0 – 10000 = \\((1 + 0.01)^{1000000}\\) – 10000 By using binomial theorem, = \\(^{1000000}C_0\\) + \\(^{1000000}C_1 (0.01)\\)\u00a0 + \\(^{1000000}C_2 (0.01)^2\\)\u00a0 + …… + \\(^{1000000}C_{1000000} (0.01)^{1000000}\\) – 10000 = (1 + 1000000(0.01) + other positive terms) – 10000 = (1 + 10000 + other positive terms) – 10000 = 1 + …<\/p>\n

Which is larger \\((1.01)^{1000000}\\) or 10,000?<\/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":"\nWhich is larger \\((1.01)^{1000000}\\) or 10,000?<\/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\/which-is-larger-1-011000000-or-10000\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Which is larger \\((1.01)^{1000000}\\) or 10,000?\" \/>\n<meta property=\"og:description\" content=\"Solution : We have, ((1.01)^{1000000})\u00a0 – 10000 = ((1 + 0.01)^{1000000}) – 10000 By using binomial theorem, = (^{1000000}C_0) + (^{1000000}C_1 (0.01))\u00a0 + (^{1000000}C_2 (0.01)^2)\u00a0 + …… + (^{1000000}C_{1000000} (0.01)^{1000000}) – 10000 = (1 + 1000000(0.01) + other positive terms) – 10000 = (1 + 10000 + other positive terms) – 10000 = 1 + … Which is larger ((1.01)^{1000000}) or 10,000? 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