Question

câu 7: tính T=(1/2-1/3)(1/2-1/5)(1/2-1/7)....(1/2-1/99)

Answer 1

\(T=(\frac{1}{2}-\frac{1}{3})(\frac{1}{2}-\frac{1}{5})(\frac{1}{2}-\frac{1}{7}).....(\frac{1}{2}-\frac{1}{99})\)

\(\implies T=\frac{1}{2}(1-\frac{2}{3}).\frac{1}{2}(1-\frac{2}{5}).\frac{1}{2}(1-\frac{2}{7}).....\frac{1}{2}(1-\frac{2}{99})\)

Thấy T có: (99-3):2+1=49(SH)

\(\implies T=(\frac{1}{2}.49).[(1-\frac{2}{3}).(1-\frac{2}{5})...(1-\frac{2}{99})\)

\(\implies T=\frac{49}{2}.\frac{1}{99}=\frac{49}{198}\)