Question

1/1×2+1/2×3+1/3×4+1/4×5+…+1/n（n+1）=？

Answer 1

解：原式=1/1-1/2+1/2-1/3+1/3-1/4+…+1/n-1/[n+1]
=1-1/[1+n]
=n/[n+1]
分析：1/1*2=1-1/2
1/2*3=1/2-1/3
从而得解

Answer 2

1/1×2+1/2×3+1/3×4+1/4×5+…+1/n（n+1）
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+......+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)

Answer 3

=1-1/2+1/2-1/3+1/3.....................+1/n-1/n+1
=1-1/n+1
=n+1/n+1-1/n+1
=n/n+1

Answer 4

1/1×2+1/2×3+1/3×4+1/4×5+…+1/n（n+1）
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+…+1/n-1/（n+1）
=1--1/（n+1）
=n/(n+1）

Answer 5

是(1/2)×3,还是1/（2×3）?