Question

Tính: \(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+...+\frac{1}{91\times93}\)

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Answer 1

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{91.93}\)

\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}\right)+\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}\right)+\frac{1}{2}.\left(\frac{1}{5}-\frac{1}{7}\right)+...+\frac{1}{2}.\left(\frac{1}{91}-\frac{1}{93}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{91}-\frac{1}{93}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{93}\right)\)

\(=\frac{1}{2}.\frac{92}{93}\)

\(=\frac{46}{93}\)

Answer 2

\(\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{91.93}\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{91}-\frac{1}{93}\right)\)

\(=\frac{1}{2}.\left(1-\frac{1}{93}\right)\)

\(=\frac{1}{2}.\frac{92}{93}\)

\(=\frac{46}{93}\)

Answer 3

lie

Answer 4

1/1*3+1/3*5+1/5*7+,,,+1/91*93

Muốn đưa về phân cách phân tích như bài 5 ta phải tìm cách đưa tử số về là 2. Ta làm như sau:

A x 2 = 2/1 x3 + 2/ 3 x 5 + 2/ 5 x 7 + ................. + 2/ 2013 x 2015

= 1/1 – 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + .................. + 1/2013 – 1/2015

= 1 – 1/2015 = 2014/2015

Vậy A = 2014/2015 : 2 = 2014/4030.

Answer 5

Cảm ơn bạn nha!