累加号上标∞下标k=0,e的-k次方?

0≤k≤+∞ ∑e^(-k)=e^0+e^(-1)+e^(-2).+e^(-k)=e^0[1-(1/e)]^(k+1)/(1-1/e)=e/(e-1) *[1 -(1/e)]^(k+1)] 当k趋近于无穷大时,-(1/e)]^(k+1)=0 所以∑e^(-k)=e/(e-1)