Đáp án:
Giải thích các bước giải:
1/2^2<1/1.2
1/3^2<1/2.3
1/4^2<1/3.4
............................
1/n^2<1/(n-1)n
=>1/2^2 + 1/3^2 +1/4^2 +...+1/n^2<1/1.2+1/2.3+1/3.4+...1/(n-1)n
<1-1/2+1/2-1/3+1/3-1/4+...+1/(n-1)-1/n=1-1/n<1(đpcm)
1/4^2 +1/6^2 + 1/8^2 +...+ 1/(2n)^2=1/(2.2)^2+1/(2.3)^2+1/(2.4)^2+...+1/(2n)^2
=1/(2^2)(2^2)+1/(2^2)(3^2)+1/(2^2)(4^2)+...+1/(2^2)(n^2)
=1/4.(2^2)+1/4(3^2)+1/4(4^2)+..+1/4(n^2)
=1/4(1/2^2+1/3^2+1/4^2+...+1/n^2)
ở câu a ta đã cm đc 1/2^2+1/3^2+1/4^2+...+1/n^2<1
=>1/4(1/2^2+1/3^2+1/4^2+...+1/n^2)<1/4.1=1/4(đpcm)
