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Arithmetico-Geometric Progression

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Question

The sum to infinity of the series 1+23+632+10333+1434+..is

Moderate
Solution

Let S be the sum of the given series i.e., 

 S=1+23+632+1033+1434+.to (S1)=23+632+1033+1434+to----i (S1)×13=232+633+1034+to-----ii

Subtracting (ii) from (i), we get 

23(S1)=23+432+433+434+to 

 23(S1)=23+43211323(S1)=23+23S=3


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The sum to infinity of the series S=1+23+632+1033+1434+is


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