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Question

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

A
781(1791020)
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B
79(991020)
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C
781(179+1020)
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D
79(99+1020)
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Solution

The correct option is C 781(179+1020)
S=0.7+0.77+0.777+upto 20 terms
=710+77102+777103+upto 20 terms
=7[110+11102+111103+upto 20 terms]
=79[(1110)+(11102)+(11103)++upto 20 terms]
=79[(1+1++upto 20 terms)(110+1102+1103++upto 20 terms)]
=7920110{1(110)20}1110
=79[2019{1(110)20}]
=79[1799+19(110)20]=781[179+(10)20]

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