Question

a) Tính tổng

b) Chứng minh rằng: 

Giúp mình với ạ

Answer 1

a: M=6/5+3/2(2/35+2/63+...+2/9603+2/9999)

=6/5+3/2*(1/5-1/7+1/7-1/9+...+1/97-1/99+1/99-1/101)

=6/5+3/2*96/505

=150/101

b: \(S=\dfrac{1}{4}\left(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{n^2}\right)\)

=>\(S< \dfrac{1}{4}\cdot\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{n-1}-\dfrac{1}{n}\right)\)

=>\(S< \dfrac{1}{4}\cdot\dfrac{n-1}{n}< \dfrac{1}{4}\)