Question

Bài 1 :

     a, \(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{101\times102}\)

     b, \(\frac{5}{5\times10}+\frac{5}{10\times15}+...+\frac{5}{115\times120}\)

     c, \(\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+...+\frac{2}{997\times999}\)

Answer 1

A.  = 1/2-1/3+1/3-1/4+1/4-1/5...+1/101-1/102=1/2-1/102=25/51.

B.  =1/5-1/10+1/10-1/15+...+1/115-1/120=1/5-1/120=23/120.

C.  = 1/5-1/7+1/7-1/9+1/9-1/11+...+1/997-1/999=1/5-1/999=994/4995.

Minh kiem tra bang may tinh roi do.

Answer 2

\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{101\times102}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{101}-\frac{1}{102}+\frac{1}{102}\)

\(=1-\frac{1}{102}\)

\(=\frac{101}{102}\)