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Question

The sum of 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
S=79[0.9+0.99+0.999+...upto 20 terms
9S7=(10.1)+(10.01)+(10.001)+...
9S7=20[110+1100+11000+...upto 20 terms]
=20110⎜ ⎜ ⎜ ⎜ ⎜1(110)201110⎟ ⎟ ⎟ ⎟ ⎟
9S7=20110209
S=781[179+1020]

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