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- Modify the power series ln ( 1 + x ) = x − x 2/ 2 + x 3/ 3 − x 4 /4 + x 5/ 5 − … to find a power series for ln ( 1 + x )/ x. Then use your power series for ln( 1 + x) /x to find the power series of the antiderivative ∫ ln ( 1 + x )/ x d x.By the alternating series test, the series converges. Find its sum and the first partial fraction decomposition. Find the limit of the partial sums.3) Express F in terms of functions that you know the power series expansion for.