so sánh
B= 1/3 + 1/3^2 + 1/3^3 + ... + 1/3^2015 với 1/2
so sánh
1/3^1+1/3^2+1/3^3+...+1/3^2015+1/3^2016 với 1/4
Cho S=1/5+2/5^2+3/5^3+4/5^4+....+2015/5^2015 . Hãy so sánh S với 1/3
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Cho M=\(\frac{\sqrt{2}-\sqrt{1}}{1+1}+\frac{\sqrt{3}-\sqrt{2}}{2+3}+\frac{\sqrt{4}-\sqrt{3}}{3+4}+...+\frac{\sqrt{2015}-\sqrt{2014}}{2014+2015}\)
Hãy so sánh M với 1/2
cho A=1*2*3+1/2*3*4+1/3*4*5+...+1/2014*2015*2016.so sánh A với 1/4
A=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)
A=\(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2014.2015}-\frac{1}{2015.2016}\right)\)
A=\(\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2015.2016}\right)\)
A=\(\frac{1}{4}-\frac{1}{2015.2016.2}\)\(\Rightarrow A<\frac{1}{4}\)
So sánh S= 1/2^2+2/2^3+3/2^4+...+n/2^n+1+...+2015/2^2016 với 1
so thu 2015 trong day so sau la so nao ?
1/1 ;2/1 ;1/2; 3/1; 2/2 ;1/3; 4/1 ;3/2; 2/3; 1/4; 5/1 ; 4/2; 3/3 ....
So sánh: \(1+\frac{1}{2}+\frac{2}{2^2}+\frac{3}{2^3}+..............+\frac{2014}{2^{2014}}+\frac{2015}{2^{2015}}\) với 3
So sánh P với 1/2 biết P=3/(1!+2!+3!) + 4/(2!+3!+4!) + ...+ 2017/(2015!+2016!+2017!) = 2
so sánh A= 1/1 x 2 x 3 + 1/2 x 3 x 4 + 1/3 x 4 x 5 + ...+ 1/ 2014 x 2015 x 2016 với 1/4
2A=2/1.2.3 + 2/2.3.4 + 2/3.4.5 + ...+2/2014.2015.2016
Ta có: 2/1.2.3=1/1.2-1/2.3; 2/2.3.4=1/2.3-1/3.4; 2/3.4.5=1/3.4-1/4.5; ....; 2/2014.2015.2016=1/2014.2015-1/2015.2016
=> 2A=1/1.2-1/2015.2016
=> 2A < 1/2 => A < 1/4