Question

A=1/90-1/72-1/56-1/42-1/30-1/20-1/12-1/6-1/2

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Answer 1

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Answer 2

A = \(\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-...-\frac{1}{6}-\frac{1}{2}\)

     = \(\frac{1}{90}-\left(\frac{1}{72}+\frac{1}{56}+...+\frac{1}{6}+\frac{1}{2}\right)\)

     = \(\frac{1}{90}-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{56}+\frac{1}{72}\right)\)

     = \(\frac{1}{90}-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{7.8}+\frac{1}{8.9}\right)\)

     = \(\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)

     = \(\frac{1}{90}-\left(1-\frac{1}{9}\right)\)

     = \(\frac{1}{90}-\frac{8}{9}\)

     = \(-\frac{79}{90}\)

Answer 3

\(A=\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)
\(A=\frac{1}{90}-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)\)
\(A=\frac{1}{90}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)\)
\(A=\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-........-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)\)
\(A=\frac{1}{90}-\left(1-\frac{1}{9}\right)\)
\(A=\frac{1}{90}-\frac{8}{9}\)
\(A=\frac{1}{90}-\frac{80}{90}\)

\(A=-\frac{79}{90}\)

Nguồn :Câu hỏi của Nguyễn Thị Bích Vân - Toán lớp 7 - Học toán với OnlineMath

_Minh ngụy_

Answer 4

A = 1/90 - 1/72 - 1/56 - 1/42 - 1/30 - 1/20 - 1/12 - 1/6 - 1/2

A = 1/90 - ( 1/72 + 1/56 + 1/42 + 1/30 + 1/20 + 1/12 + 1/6 + 1/2)

A = 1/90 - ( 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72)

A = 1/90 - ( 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9)

A = 1/90 - ( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/8 - 1/9)

A = 1/90 - ( 1 - 1/9)

 A = 1/90 - 8/9

A = 1/90 - 80/90 = -79/90

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