Question

Tính :\(A=\frac{5}{1\times2}+\frac{5}{2\times3}+\frac{5}{3\times4}+....+\frac{5}{99\times100}\)Ai nhanh mik tick nha^_-

Answer 1

\(\Rightarrow A=5\left(\frac{1}{1x2}+\frac{1}{2x3}+...+\frac{1}{99x100}\right)\)

\(\Rightarrow A=5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(\Rightarrow A=5\left(1-\frac{1}{100}\right)\)

\(\Rightarrow A=\frac{5x99}{100}=\frac{99}{20}\)

Answer 2

\(A=\frac{5}{1}-\frac{5}{2}+\frac{5}{2}-\frac{5}{3}+\frac{5}{3}-\frac{5}{4}+....+\frac{5}{99}-\frac{5}{100}\)

\(A=\frac{5}{1}+\left(-\frac{5}{2}+\frac{5}{2}\right)+\left(-\frac{5}{3}+\frac{5}{3}\right)+\left(-\frac{5}{4}+\frac{5}{4}\right)+...\left(-\frac{5}{99}+\frac{5}{99}\right)+\frac{5}{100}\)

\(A=\frac{5}{1}+0+0+....+0+\frac{5}{100}\)

\(A=\frac{500}{100}+\frac{5}{100}=\frac{205}{100}=\frac{101}{20}\)

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Answer 3

bạn devil girl làm đúng rồi

Answer 4

thang ad dragon boy ngu nhu cho

Answer 5

À xin lỗi

Phải là 

\(\frac{5}{1}+0+0+......+0-\frac{5}{100}\)

\(=\frac{500}{100}-\frac{5}{100}=\frac{495}{100}=\frac{99}{20}\)

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Answer 6

bạn ad dragon boy ơi,làm lại dấu cũng sai rồi kìa

Answer 7

bằng \(\frac{99}{20}\)nha bạn 

ai k mk mk k cho

Answer 8

ad dragon boy sai bet roi

Answer 9

bang \(\frac{99}{20}+0\)