Question

chứng tỏ rằng:1/2mu2+1/3mu2+1/4mu2+....+1/2014mu2+1/2015mu2<1                               

lề:mjh k pjt vjet dau fan so va dau mu nen vjet vay nhe

p/s:cac ban gjaj gjup mjh vs,aj co nhu cau ket ban vs mjh k nk

 

Answer 1

Đặt A =\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+...+\frac{1}{2015^2}\)

A < \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2014.2015}\)

A < \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2014}-\frac{1}{2015}\)

A < \(1-\frac{1}{2015}\)< \(1\)

=> A < 1 (đpcm)