is it true that 1-1/2+1/3-1/4=....=ln2??
how i solve that question i have to use the harmonic series!?
Thanks
Nana
Starting from the geometric series...
$\displaystyle \frac{1}{1+x} = 1 - x + x^{2} - x^{3} + ...$ , $\displaystyle |x|<1$ (1)
... and integrating term by term we obtain...
$\displaystyle \ln (1+x) = x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \frac{x^{4}}{4} + ...$ (2)
Setting in (2) x=1 we have...
$\displaystyle \ln 2 = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + ...$ (3)
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$