Question

Tính tổng

M=1/2.3/4.4/5.......99/100

N=2/3.4/5.5/6.....100/101

Answer 1

\(M=\frac{1}{2}.\frac{3}{4}.\frac{4}{5}...\frac{99}{100}\)

\(\Leftrightarrow M=\frac{1}{2}.\frac{3.4...99}{4.5...100}\)

\(\Leftrightarrow M=\frac{1}{2}.\frac{3}{100}\)

\(\Leftrightarrow M=\frac{3}{200}\)

\(N=\frac{2}{3}.\frac{4}{5}.\frac{5}{6}...\frac{100}{101}\)

\(\Leftrightarrow N=\frac{2}{3}.\frac{4.5...100}{5.6...101}\)

\(\Leftrightarrow N=\frac{2}{3}.\frac{4}{101}\)

\(\Leftrightarrow N=\frac{8}{303}\)