Toán Lớp 6: A=1/1.2 + 1/2.3 + -. + 1/99.100 B=1/1.3 + 1/3.5 + -. + 1/2009.2011

Question

Toán Lớp 6:  A=1/1.2 + 1/2.3 + ..... + 1/99.100 B=1/1.3 + 1/3.5 + ..... + 1/2009.2011

tonhu12 · Answer

1)   ta c&oacute; $ frac{1}{1.2}$ = $ frac{1}{1.}$ - $ frac{1}{2}$ = 1 - $ frac{1}{2}$   Tương tự: $ frac{1}{2.3}$ = $ frac{1}{2}$ - $ frac{1}{3}$   =>  A=1/1.2 + 1/2.3 + ..... + 1/99.100 = 1 - $ frac{1}{2}$ + $ frac{1}{2}$ - $ frac{1}{3}$ + ... + $ frac{1}{99}$ - $ frac{1}{100}$      A = 1 - $ frac{1}{100}$ = $ frac{99}{100}$     2)   ta c&oacute;: 1/1.3 = (1/1 - 1/3) :2 = 1/2 - 1/6      Tương tự: 1/3.5 = (1/3 - 1/5):2 = 1/6 - 1/10     => B = 1/2 - 1/6 +1/6 - 1/10 + ... + 1/4018 - 1/ 4022     => B = 1/2 - 1/4022 = 1005/2011

minhtuquynh · Answer

A = 1/(1.2) + 1/(2.3) + ... + 1/(99.100)   = 1 - 1/2 + 1/2 - 1/3 +  .... + 1/99 - 1/100   = 1 - 1/100   = 99/100   Vậy A= 99/100      B= 1/(1.3) + 1/(3.5) + ... + 1/(2009 . 2011)   = 1/2 . ( 2/(1.3) + 2/(3.5) + .... + 2/(2009. 2011))   = 1/2 . ( 1 - 1/3 + 1/3 - 1/5 + ... + 1/2009 - 1/2011)   = 1/2 . ( 1 - 1/2011)   = 1/2 . 2010/2011   =  1005/2011   Vậy B = 1005/2011