The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,...., is
A
781(179−10−20)
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B
79(99−10−20)
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C
781(179+10−20)
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D
79(99+10−20)
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Solution
The correct option is C781(179+10−20) Given sequence can be written as 710+77100+777103+...+ up to 20 terms =7[110+11100+111103+...+upto20terms] Multiply and divide by 9 79[(1−110+(1−1102)+(1−1103))+.....upto20terms]=79[20−110(1−(110)20)1−110]=79[1799+19(110)20]=781[179+(10)−20]