Question

a. 1/1×2+1/2×3+…+1/n×(n+1)    ( n€n ,n>2)

 

Answer 1

1/1x2 + 1/2x3 + ... + 1/nx(n+1)

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

= 1 - 1/n+1

= n/n+1

Answer 2

a/ \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{n.\left(n+1\right)}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{n}-\frac{1}{n+1}\)

\(=\frac{n}{n+1}\)

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