Question

Rút gọn biểu thức với n\(\in\)N; n\(\ge\)2

A=\(\frac{2^2-1}{2^2}.\)\(...\frac{3^2-1}{3^2}.\frac{4^2-1}{4^2}\)\(....\frac{n^2-1}{n^2}\)

Help meeee.....cần gấpppppp :((

Answer 1

Dấu "....." ở giữa \(\frac{2^2-1}{2^2}\) và \(\frac{3^2-1}{3^2}\) là gì vậy?

Answer 2

\(A=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}.....\frac{\left(n-1\right)\left(n+1\right)}{n^2}=\frac{\left(1.2.3.....\left(n-1\right)\right)\left(3.4.5......\left(n+1\right)\right)}{\left(2.3.4.....n\right)\left(2.3.4......n\right)}=\frac{1.\left(n+1\right)}{n.2}=\frac{n+1}{2n}\)