The sum of first 20terms of the sequence 0.7, 0.77, 0.777, .. , is(1) – InterviewSolution

InterviewSolution

1.	The sum of first 20terms of the sequence 0.7, 0.77, 0.777, .. , is(1) `7/9(99-10^(-20))`(2)`7/(81)(179+10^(-20))`(3) `7/9(99+10^(-20))`(3)`7/(81)(179-10^(-20))`A. `7/81(179-10)^(20))`B. `7/9(99 -10^(20))`C. `7/81(179 +10^(-20))`D. `7/9(99+10^(-20))`
Answer» Correct Answer - C 0.7+0.77+0.777+….+0.7777….7 `=7/9[0.9+0.99+0.999+….+0.999…9]` `=7/9[(1-0.1)+(1-0.01)+(1-0.001)+….+(1-0.000…1)]` `=7/9[20-1/10cdot(1-1/10^(20))/(1-1/10)]=7/9[20-1/9cdot((10^(20)-1)/10^(20))]` `=7/81[180-(1-1/10^(20))]=7/81[179+10^(-20)]`

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