momo1729 24.04.2011 20:09 Find all positive integers n such that : $-2^{0}+2^{1}-2^{2}+2^{3}-2^{4}+...-(-2)^{n}=4^{0}+4^{1}+4^{2}+...+4^{2010}$
pco 24.04.2011 20:24 momo1729 wrote: Find all positive integers n such that : $-2^{0}+2^{1}-2^{2}+2^{3}-2^{4}+...-(-2)^{n}=4^{0}+4^{1}+4^{2}+...+4^{2010}$ So $\frac{(-2)^{n+1}-1}3=\frac{4^{2011}-1}3$ and so $\boxed{n=4021}$