0.2 + 0.22 + 0.222 + … upto n terms is equal to

Question

0.2 + 0.22 + 0.222 + … upto n terms is equal to, 2 9 - 2 81 1 - 10 - n, n 1 9 1 - 10 - n, 2 9 n - 1 9 1 - 10 - n, 2 9

MARKS App · Accepted Answer

0.2 + 0.22 + 0.222 + . . . n terms = 2 0.1 + 0.11 + 0.111 + … n t e r m s = 2 1 10 + 11 100 + 111 1000 + … n t e r m s = 2 9 9 10 + 99 100 + 999 1000 + … n t e r m s = 2 9 1 - 1 10 + 1 - 1 100 + 1 - 1 1000 + … n t e r m s = 2 9 n - 1 10 + 1 100 + 1 1000 + … n = 2 9 n - 1 10 1 - 1 10 n 1 - 1 10 = 2 9 n - 1 10 × 10 9 . 10 n - 1 10 n = 2 9 n - 1 9 1 - 10 - n

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