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Question

Sum 1+3x+5x2+7x3+9x4+.... to infinity.

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Solution

Let S=1+3x+5x2+7x3......
Multiplying both sides by a, we get
Sx=0+x+3x2+5x3.......
Subtract both eqns, we get
S(1x)=1+2(x+x2+x3.......)
Clearly, the series in the bracket is a G.P. with common ratio =x
S(1x)=1+2x1x=1+x1x
S=1+x(1x)2

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