Question

[Đỗ Yến Nhi]

Tính giá trị của biểu thức:

B= 9/ 1. 2- 9/ 2.3-.....- 9/ 99. 100

Answer 1

[zZz Cool Kid_new zZz]

\(B=\frac{9}{1\cdot2}-\frac{9}{2\cdot3}-.....-\frac{9}{99\cdot100}\)

\(=\frac{9}{2}-9\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+....+\frac{1}{99\cdot100}\right)\)

\(=\frac{9}{2}-9\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+......+\frac{1}{99}-\frac{1}{100}\right)\)

\(=\frac{9}{2}-9\left(1-\frac{1}{100}\right)\)

\(=\frac{9}{2}-\frac{891}{100}\)

tự tính nốt.

Answer 2

[Trần Tiến Pro ✓]

\(B=\frac{9}{1.2}-\frac{9}{2.3}-.....-\frac{9}{99.100}\)

\(B=\frac{9}{1.2}+\frac{-9}{2.3}+\frac{-9}{3.4}+....+\frac{-9}{99.100}\)

\(B=\frac{9}{2}+\left(-9\right)\left(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}\right)\)

\(B=\frac{9}{2}+\left(-9\right).\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\right)\)

\(B=\frac{9}{2}+\left(-9\right).\left(1-\frac{1}{100}\right)\)

\(B=\frac{9}{2}+\left(-9\right).\frac{99}{100}\)

\(B=\frac{9}{2}+\frac{-891}{100}\)

\(B=\frac{450}{100}+\frac{-891}{100}\)

\(B=\frac{-441}{100}\)