Cho A=1/3^2+1/4^2+1/5^2+...+1/50^2
Chung to rang 1/4<M<4/9
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Cho A=1/3^2+1/4^2+1/5^2+...+1/50^2
Chung to rang a,A>1=4 b,A>4/9
Cho A=1/3^2+1/4^2+1/5^2+...+1/50^2
Chung to rang a,A>1=4 b,A>4/9
Cho A=1/3^2+1/4^2+1/5^2+...+1/50^2
Chung to rang 1/4<M<4/9
Cho A=1/3^2+1/4^2+1/5^2+...+1/50^2
Chung to rang 1/4<M<4/9
cho a=1=1\2+1\3-1\4+1\5...+1\49-1\50.Chung to rang 7\12<4<5\6
cho P=1+1/2+1/3+1/4+...+1/2^100-1. chung to rang P<50
cho S = 1/ 2^2 + 1/ 3^2 + 1/ 4^2 + 1/5^2 +... + 1/ 2016 ^ 2 . chung to rang S< 1
Ta có:
1/1^2 + 1/3^2 + 1/4^2 + ...+ 1/2016^2
= 1/2.2 + 1/3.3 + 1/4.4 + ... + 1/2016.2016
S < 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/2015.2016
S < 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2015 - 1/2016
S < 1 - 1/2016
Mà 1 - 1/2016 < 1
=> S < 1
Vậy A < 1
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a,A=1/1^2+1/2^2+1/3^2+1/4^2+...+1/50^2.chung minh rang a<2
b;2^1+2^2+2^3+...+2^30.chung minh rang B chia het cho21
chung minh rang:1/(1*2)+1/(3*4)+1/(5*6)+.....+1/(49*50)=1/26+1/27+1/28+....+1/50