Question

Tính

\(\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}+......+\frac{1}{97.99}\)

Tính hộ mik với

Answer 1

\(\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}+......+\frac{1}{97.99}\)

=\(\frac{1}{2}.\left(\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}+......+\frac{2}{97.99}\right)\)

=\(\frac{1}{2}.\left(\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+......+\frac{1}{97}-\frac{1}{99}\right)\)

=\(\frac{1}{2}.\left(\frac{1}{9}-\frac{1}{99}\right)=\frac{1}{2}.\left(\frac{11}{99}-\frac{1}{99}\right)=\frac{1}{2}.\frac{10}{99}=\frac{5}{99}\)