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Question

The sum to infinite terms of the series
1+23+632+1033+1434 is

A
3
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B
4
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C
6
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D
2
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Solution

The correct option is A 3
We have
S=1+23+632+1033+1434+ ...(i)
Multiplying both sides by 13 we get
13S=13+232+633+1034+ ...(ii)
Subtracting eqn. (ii) from eqn. (i) we get
23S=1+13+432+433+434+23S=43+432+433+434+23S=43113=43×32S=3

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