tính T=\(\left(\frac{1}{2}-\frac{1}{3}\right)\left(\frac{1}{2}-\frac{1}{5}\right)\left(\frac{1}{2}-\frac{1}{7}\right)...\left(\frac{1}{2}-\frac{1}{99}\right)\)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(T=\left(\frac{1}{2}-\frac{1}{3}\right)\left(\frac{1}{2}-\frac{1}{5}\right)\left(\frac{1}{2}-\frac{1}{7}\right).....\left(\frac{1}{2}-\frac{1}{99}\right)\)
\(T=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}-\frac{1}{7}-........-\frac{1}{99}\right)\)
\(T=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-..........-\frac{1}{99}\right)\)
\(T=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{99}\right)\)
\(T=\frac{1}{2}\left(\frac{99}{297}-\frac{3}{297}\right)\)
\(T=\frac{1}{2}.\frac{96}{297}\)
\(T=\frac{1}{2}.\frac{32}{99}\)
\(T=\frac{16}{99}\)
\(T=\left(\frac{1}{2}-\frac{1}{3}\right)\left(\frac{1}{2}-\frac{1}{5}\right)\left(\frac{1}{2}-\frac{1}{7}\right)\cdot.....\cdot\left(\frac{1}{2}-\frac{1}{99}\right)\)
\(=\frac{1}{2\cdot3}\cdot\frac{3}{2\cdot5}\cdot\frac{5}{2\cdot7}\cdot.....\cdot\frac{97}{2\cdot99}\)
\(=\frac{1\cdot3\cdot5\cdot.....\cdot97}{2^{49}\left(3\cdot5\cdot7\cdot....\cdot99\right)}=\frac{1}{2^{49}\cdot99}\)