Question

So sánh 1/2*1/2+1/3*1/3+1/4*1/4+...+1/50*1/50 với 1

Answer 1

Gọi tổng trên là A

A = 1/2²+1/3³+.....+1/50²

A = 1/2.2 + 1/3.3 +.....+ 1/50.50

A < 1/1.2 + 1/2.3 +.....+ 1/49.50

A < 1 - 1/2 + 1/2 - 1/3 +.......+ 1/49 - 1/50

A < 1 - 1/50

A < 49/50 < 1
=> A < 1

Ai k mk mk k lại 

Answer 2

A=(1/2)*(1/2)+(1/3)*(1/3)+...+(1/50)*(1/50) = 1/(2*2)+1/(3*3)+1/(4*4)+...+1/(50*50) < 1/(1*2)+1/(2*3)+...+1/(49*50)

 Mà 1/(1*2)+1/(2*3)+...+1/(49*50) = 1-1/2+1/2-1/3+1/3-1/4+...+1/49-1/50 =1-1/50 <1                                                 

=> A<1