Question

1/1.2.3+1/2.3.4+1/3.4.5+....+1/49.50.51

Giải nhanh giúp mình với , cái dấu / là vạch giữa tử và mẫu

Answer 1

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{49.50.51}\)

\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-....-\frac{1}{50.51}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{2550}\right)=\frac{637}{2550}\)

Answer 2

\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{49.50.51}\)

\(2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{49.50.51}\)

ta có dạng tổng quát

\(\frac{1}{n\left(n+1\right)}-\frac{1}{\left(n+1\right)-\left(n+2\right)}=\frac{2}{n\left(n+1\right)\left(n+2\right)}\) bạn quy đồng ra rồi tính nha

\(2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+.....+\frac{1}{49.50}-\frac{1}{50.51}\)

\(2A=\frac{1}{1.2}-\frac{1}{50.51}\)

\(2A=\frac{637}{1275}\)

\(A=\frac{637}{2550}\)

Answer 3

= 1/2 (1/1.2 - 1/50.51)

=......