Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series

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

Options

A7 81 (179+10⁻²⁰ )
B7 9 (99+10⁻²⁰ )
C7 81 (179-10⁻²⁰ )
D7 9 (99-10⁻²⁰ )

Correct answer

A. 7 81 (179+10⁻²⁰ )

Step-by-step solution

aligned & .7+.77+.777+------ & .= 7 9 (.9+.99+.999+-----)= 7 9 [1-.1)+(1-.01)+(1-.001) . . . upto n times ] & = 7 9 (20- 1 9 +10⁻²⁰ ) & = 7 81 (179+10⁻²⁰ ) aligned

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