Question

\(A=\left(\frac{1}{2^2}-1\right).\left(\frac{1}{3^2}-1\right).\) \(...\)\(.\left(\frac{1}{100^2}-1\right)\)tính A

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ai nhanh mk tk cho

Answer 1

\(A=\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}....\frac{100^2-1}{100^2}\)

\(A=\frac{1.3}{2^2}.\frac{2.4}{3^2}....\frac{99.101}{100^2}\)

\(A=\frac{1.3.2.4...99.100}{2.2.3.3...100.100}\)

\(A=\frac{1.2...99}{2.3....100}.\frac{3.4...101}{2.3...100}\)

\(A=\frac{1}{100}.\frac{101}{2}\)

\(A=\frac{101}{200}\)