Question

\(y=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{4.5}+.......+\frac{1}{99.100}\)

\(B=\frac{1}{50}+\frac{1}{51}+\frac{1}{52}+.......+\frac{1}{100}\)

TÍNH GIÁ TRỊ CỦA : Y - B = ?

Answer 1

\(y=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{4.5}+.......+\frac{1}{99.100}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

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

\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)-\left(1+\frac{1}{2}+...+\frac{1}{50}\right)=\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\)

=>y=B

=>y-B=0

Answer 2

y=\(y=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}......+\frac{1}{99}-\frac{1}{100}=\frac{1}{1}-\frac{1}{100}=\frac{100}{100}-\frac{1}{100}=\frac{99}{100}\)

vay ket =\(\frac{99}{100}\)

Answer 3

con lai tu tinh nhe