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=431−13=43×32⇒S=3