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ind integrals
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Your question needs to be revised slightly. The last term in the summation is 2nx2n-1. Also, i feel the stipulation that |x|<1 has also to be specified. Oops! you have already sort of done that. Consider F(x) = x2+x4+...+x2n  2rx2r-1 = dF(x)/dxr=1,n f(x) = lim(n  inf) dF(x)/dxSince, we know that dF/dx is a convergent sum,  lim(ninf) dF(x)/dx dx = lim(ninf)dF/dx dx = lim(ninf) F(x) = x2/1-x2. |
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