Question

1.CMR:\(1+\frac{1}{2^3}+...+\frac{1}{n^3}>\frac{5}{4}\)vs mọi n nguyên dương

Answer 1

A< 1+1/(2³-2)+1/(3³-3)+...+1/(n³-n)

Đặt B=1/(2³-2)..... =>B=1/1.2.3+1/2.3.4+...+1/(n-1)n(n+1) =1/2.(1/1.2-1/2.3+1/2.3-1/3.4+1/3.4....-1/n(n+1))

                                  =1/2.(1/2-1/n(n+1))=1/4-1/2.n.(n+1)<1/4

=>B<1/4 =>A=B+1<(1/4)+1

 =>A<5/4

Answer 2

999 - 888 - 111 + 111 - 111 + 111 - 111

= 111 - 111 + 111 -111 + 111 - 111

= 0 + 111 - 111 + 111 - 111

= 111 - 111 + 111 - 111

= 0 + 111 - 111

= 111 - 111

= 0

Đáp số: 0