\(Tổng=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}=1-\frac{1}{100}=\frac{99}{100}\)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)
\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)
\(1-\frac{1}{100}\)
\(=\frac{99}{100}\)
Vậy: \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}=\frac{99}{100}\)
Bạn sai đề rồi đề phải thế này nè:
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{.1}{3.4}+...+\frac{1}{99.100}\)
\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(\Leftrightarrow1-\frac{1}{100}\)
\(=\frac{99}{100}\)
ta đặt biểu thứ là :
A = 1/1x2 + 1/2x3 + 1/3x4 + ..... + 1/99x100
A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ..... + 1/99 - 1/100
A = 1 - 1/100
A = 99/100
