The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, is: - Mathematics MCQ JEE Main 2026 | ExamTest.live

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The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, \dots is:

Solution & Step-by-step Explanation

S = 0.7 + 0.77 + 0.777 + \dots (20 terms) S = 7 [0.1 + 0.11 + 0.111 + \dots] = \frac{7}{9} [0.9 + 0.99 + 0.999 + \dots] S = \frac{7}{9} [(1 - 0.1) + (1 - 0.01) + (1 - 0.001) + \dots] S = \frac{7}{9} [20 - (0.1 + 0.01 + 0.001 + \dots to 20 terms)] S = \frac{7}{9} [20 - \frac{0.1 ( 1 - 0. 1 ^{20} )}{1 - 0.1}] = \frac{7}{9} [20 - \frac{1}{9} (1 - 1 0^{- 20})] S = \frac{7}{9} [\frac{180 - 1 + 1 0 ^{- 20}}{9}] = \frac{7}{81} [179 + 1 0^{- 20}] .

Try it yourself before checking the explanation above.

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, \dots is:

\frac{7}{9} (99 - 10^{-20})

\frac{7}{81} (179 + 10^{-20})

\frac{7}{9} (99 + 10^{-20})

\frac{7}{81} (179 - 10^{-20})

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