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Question

The sum of the series 1+2x+3x2+4x3+..... upto n terms is

A
1(n+1)xn+nxn+1(1x)2
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B
1xn(1x
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C
xn+1
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D
None of these
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Solution

The correct option is A 1(n+1)xn+nxn+1(1x)2
Let Sn be the sum of the given series to n terms, then
Sn=1+2x+3x2+4x3+....+nxx1 ....(i)

xSn=x+2x2+3x2+....+nxn ....(ii)

Subtracting (ii) from (i), we get
(1x)Sn=1+x+x2+x3+.... to n terms nxn
=((1xn)(1x)nxn)
Sn=(1xn)nxn(1x)(1x)2=1(n+1)xn+nxn+1(1x)2.


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