Question

Gấp gấp mn ơi mai mik đi học rồi mà ko bt bài làm như nào cứu mik với!!!!!!

\(a.\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+.....+\dfrac{1}{99\times1000}\)

\(b.\dfrac{5}{2\times5}+\dfrac{5}{5\times8}+\dfrac{5}{8\times11}+.....+\dfrac{5}{32\times35}\)

cứu me sos

Answer 1

Sửa đề: 

`A = 1/(1xx2) + 1/(2xx3) + ... + 1/(99xx100)`

`= 1 - 1/2 + 1/2 - 1/3 + ... +1/99 - 1/100`

`= 1 - 1/100`

`= 99/100`

`B = 5/(2 xx 5) + 5/(5 xx 8) + ... + 5/(32 xx 35)`

`= 5/3 xx (3/(2 xx 5) + 3/(5 xx 8) + ... + 3/(32 xx 35))`

`= 5/3 xx (1/2 - 1/5 + 1/5 - 1/8 + ... + 1/32 - 1/35)`

`= 5/3 xx (1/2 - 1/35) `

`= 5/3 xx 33/70`

`= 11/14`

Answer 2

\(a.\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+...+\dfrac{1}{99\times100}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=1-\dfrac{1}{100}\)
\(=\dfrac{100}{100}-\dfrac{1}{100}\)
\(=\dfrac{99}{100}\)
\(b.\dfrac{5}{2\times5}+\dfrac{5}{5\times8}+\dfrac{5}{8\times11}+...+\dfrac{5}{32\times35}\)
\(3b=5\left(\dfrac{1}{2\times5}+\dfrac{1}{5\times8}+\dfrac{1}{8\times11}+...+\dfrac{1}{32\times35}\right)\)
\(3b=5.\left(\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{32}-\dfrac{1}{35}\right)\)
\(3b=5.\left(\dfrac{1}{2}-\dfrac{1}{35}\right)\)
\(3b=5.\left(\dfrac{35}{70}-\dfrac{2}{70}\right)\)
\(3b=5.\dfrac{33}{70}\)
\(3b=\dfrac{1.33}{1.14}\)
\(3b=\dfrac{33}{14}\)
\(b=\dfrac{33}{14}:3\)
\(b=\dfrac{33}{14}.\dfrac{1}{3}\)
\(b=\dfrac{11.1}{14.1}\)
\(b=\dfrac{11}{14}\)

Answer 3

`a, 1/(1 xx 2)+1/(2 xx 3) + 1/(3xx4)+...+1/(99xx100) chứ