Biết:n!=1.2.3....n
Chứng tỏ rằng :A=1/2!+2/3!+...+2013/2014!<1
Mình sẽ tick cho
Biết n! = 1.2.3. ... . n ( n \(\in\)N* )
Chứng tỏ rằng:
A = \(\frac{1}{2!}+\frac{2}{3!}+...+\frac{2013}{2014!}< 1\)
biết n! = 1.2.3....n (n thuộc N, n\(\ge\)2). chứng tỏ rằng A = \(\frac{1}{2}\)+\(\frac{2}{3}\)+ ....+ \(\frac{2013}{2014}\)< 1
Biết n!=1.2.3.....n (n> hoặc =2)
chứng tỏ rằng:A=1/2!+2/3!+.......+2013/2014!<1
Cho n! = 1.2.3.....n. Chứng minh A = 1/2! + 2/3! +...+2013/2014! < 1
\(A=\frac{1}{2!}+\frac{2}{3!}+...+\frac{2013}{2014!}=\frac{2-1}{2!}+\frac{3-1}{3!}+...+\frac{2014-1}{2014!}\)
\(=1-\frac{1}{2!}+\frac{3}{3!}-\frac{1}{3!}+...+\frac{2014}{2014!}-\frac{1}{2014!}\)
\(=1-\frac{1}{2!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{3!}-\frac{1}{4!}+...+\frac{1}{2013!}-\frac{1}{2014!}\)
\(=1-\frac{1}{2014!}
Biết: n!= 1.2.3.....n (n\(\in\)N* ; n \(\ge\)2)
A = \(\dfrac{1}{2!}+\dfrac{2}{3!}+...+\dfrac{2013}{2014!}\)< 1
Cho A = \(1.2.3...2013.2014\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2013}+\frac{1}{2014}\right)\). Chứng minh rằng A chia hết cho 2015
Bài 1:So sánh 20142014 + 1/20142015 + 1 và 20142013 + 1/20142014 + 1. Bài 2: a) chứng tỏ rằng: D=1/22 + 1/32 + 1/42 +....+1/102 < 1. b)chứng tỏ rằng: E=1/101+1/102+...+1/299+1/300>2/3.C)chứng tỏ rằng: F=1/5+1/6+1/7+...+1/17 < 2
\(D=\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+.......+\dfrac{1}{10^2}\)
\(D< \dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+.......+\dfrac{1}{9.10}\)
\(D< 1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+.....+\dfrac{1}{9}-\dfrac{1}{10}\)
\(D< 1-\dfrac{1}{10}\Leftrightarrow D< 1\left(đpcm\right)\)
Chứng tỏ rằng :
3/2^2 + 4/2^3 + ...... + 2014/2^2013 + 2015/2^2014 < 2
Biết n!=1.2.3....n
CMR A=\(\frac{1}{2!}+\frac{2}{3!}+....+\frac{2013}{2014!}< 1\)