Question

Rút gọn biểu thức:

T= (1/2+ 1).(1/3+ 1) .(1/4+ 1)....(1/98+ 1). (1/99+ 1)

Answer 1

T= (1/2+ 1).(1/3+ 1) .(1/4+ 1)....(1/98+ 1). (1/99+ 1)

T= 3/2+4/3+5/4+...+99/98+100/99

T= 100/2

T= 50

Answer 2

T=\(\left(\frac{1}{2}+1\right)\left(\frac{1}{3}+1\right)...\left(\frac{1}{99}+1\right)\)=\(\frac{3}{2}\cdot\frac{4}{3}\cdot\cdot\cdot\frac{100}{99}\)=2*100=200

Answer 3

\(T=\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right)...\left(\frac{1}{99}+1\right)\)

\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{100}{99}\)

\(=\frac{3.4.5...100}{2.3.4....99}\)

\(=\frac{100}{2}=50\)