用数学归纳法证明2×4分之1+4×6分之1+…+2

用数学归纳法证明2×4分之1+4×6分之1+…+2n乘以2n+2分之一=4n+1分之一

1个回答

1/2×4+1/4×6+……+1/2n(2n+2)
=1/4(1/1×2+1/2×3+……+1/n(n+1)]
=1/4[1-1/2+1/2-1/3+……+1/n-1/(n+1)]
=1/4(1-1/(n+1)]
=n/4(n+1)