Homework Sourse1n1n1SolutionFrom the taylor series expansion we have 1n1 xn
(-1)^(n+1)/(n+1)
Solution
From the taylor series expansion we have:
(-1)^(n+1) xn/n = ln(1+x)
So we have:
n=1 (-1)^(n) xn/n = -ln(1+x)
or
n=0 (-1)^(n+1) xn+1/(n+1) = -ln(1+x)
Now put x = 1 :
n=0 (-1)^(n+1) * 1/(n+1) = -ln(1+1) = -ln(2)
