Question

1/2*3+1/3*4+...+1/99*100

ai giúp mk sẽ tk 3 tk

Answer 1

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{99\cdot100}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{2}-\frac{1}{100}=\frac{50-1}{100}=\frac{49}{100}\)

Answer 2

1/2*3+1/3*4+.....+1/99*100

=1/2-1/3+1/3-1/4+........1/99*100

=1/2+(-1/3+1/3)+(-1/4+1/4)+.........+(-1/99+1/99)-1/100

=1/2-1/100

=50/100-1/100

=49/100