等差数列公差为d,1/a1a2+1/a2a3+.1/anan+1=?

等差数列公差为d,1/a1a2+1/a2a3+.1/anan+1=?
等差数列公差为d,1/a1a2+1/a2a3+.1/anan+1=?

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)

1/anan+1=1/an(an+d)=1/d(1/an-1/(an+d)) (裂项）
1/a1a2+1/a2a3+......1/anan+1=1/d(1/a1-1/a2+1/a2-1/a3+1/a3-1/a4+.......+1/an-1/an+1)=
1/d(1/a1-1/an+1)