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Question

The value of 0.7+0.77+0.777+ upto 20 terms 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]
Let
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)+upto 20 terms]
9S7=20[110+1100+11000+...upto 20 terms]
9S7=20110⎜ ⎜ ⎜ ⎜ ⎜1(110)201110⎟ ⎟ ⎟ ⎟ ⎟
9S7=20110209
S=781[179+1020]

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