等差数列公差为d,1/a1a2+1/a2a3+.1/anan+1=?

问题描述:

等差数列公差为d,1/a1a2+1/a2a3+.1/anan+1=?

采用裂项法的思路:(1/a1-1/a2)/d+(1/a2-1/a3)/d+.(1/an-1/an+1)/d=(1/a1-1/an+1)/d=(nd/(a1*an+1))/d=n/(a1*an+1)