$u_{n} = \frac{cos^2{1} }{1.2} + \frac{cos^2{2} }{2.3}+... \frac{cos^2{n} }{n(n+1)}$

D

dien0709

Chứng minh dãy số tăng, bị chặn trên

$U_n=\dfrac{cos^21}{1.2}+\dfrac{cos^22}{2.3}+........+\dfrac {cos^2n}{n(n+1)}$

$U_{n+1}-U_n=\dfrac{cos^2(n+1)}{(n+1)(n+2)}>0 $ với mọi $n\in N^*\to $ đpcm

$U_n< \dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{n(n+1)}=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{n}-\dfrac{1}{n+1}=\dfrac{n}{n+1}$
 
You must log in or register to reply here.
Top Bottom