Question

tinh nhanh

B=\(\dfrac{3}{1^{2^{ }}.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^{2^{ }}.4^2}+...+\dfrac{19}{9^2.10^2}\)

Answer 1

Lời giải:

\(B=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}\)

\(=\frac{2^2-1^2}{1^2.2^2}+\frac{3^2-2^2}{2^2.3^2}+\frac{4^2-3^2}{3^2.4^2}+...+\frac{10^2-9^2}{9^2.10^2}\)

\(=\frac{1}{1^2}-\frac{1}{2^2}+\frac{1}{2^2}-\frac{1}{3^2}+\frac{1}{3^2}-\frac{1}{4^2}+....+\frac{1}{9^2}-\frac{1}{10^2}\)

\(=1-\frac{1}{10^2}=\frac{10^2-1}{10^2}=\frac{99}{100}\)