Question

rút gọn : T= { 1/2 +1 } . { 1/3 +1 } . { 1/4 +1 } ... { 1/98 +1 } . { 1/99 +1 }

Answer 1

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

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

\(T=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}......\frac{100}{99}=\frac{3.4.5.6.....100}{2.3.4.5...99}=\frac{100}{2}=50\)

Vậy T = 50

Answer 2

T={1/2 + 1} .{1/3+1} . {1/4+1}....{  1/98+1].[1/99+1}

  =3/2 . 4/3 . 5/4.....99/98 . 100/99

  =1/2 . 1 . 1.....1. 100/1 (MIK RÚT GỌN CHÉO CÁC PHÂN SỐ LIỀN NHAU)

  =100/2

  =50 Nhé

Answer 3