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it is known for x ne 1 that 1+x+x^(2)+"…...

it is known for `x ne 1` that `1+x+x^(2)+"….."+x^(n-1) = (1-x^(n))/(1-x)`, hence find the sum of the series `S = 1+2x+3x^(2)+"….."+(n+1)x^(n)`.

Text Solution

Verified by Experts

The correct Answer is:
`((n-1)x^(n)-nx^(n-1)+1)/(1-x)^(2), x ne 1`
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