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

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

Tìm x biết

\(\left(\frac{1}{2}+\frac{1}{3}+....+\frac{1}{2014}+\frac{1}{2015}\right).x=\frac{2014}{1}+\frac{2013}{2}+\frac{2012}{3}+...+\frac{2}{2013}+\frac{1}{2014}\)

Biết n!=1.2.3...n \(\left(n\inℕ^∗;n\ge2\right)\)và \(A=\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+......+\frac{2014}{2015!}\)

Hãy so sánh A với 1

TínhTính giá trị của A, biết A=

\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2014}}{\frac{2013}{1}+\frac{2012}{2}+\frac{2011}{3}+...+\frac{1}{2013}}\)

\(A=\frac{\left(1-2\right).\left(1+2\right)}{2^2}.\frac{\left(1-3\right).\left(1+3\right)}{3^2}.......\frac{\left(1-2013\right).\left(1+2013\right)}{2013^2}.\frac{\left(1-2014\right).\left(1+2014\right)}{2014^2}\)

chung to A=\(\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+...+\frac{1}{2013!}<2\)

(n!=1.2.3....n duoc goi la giai thua)

So sánh M = \(\frac{2014}{1.2.3}+\frac{2014}{2.3.4}+\frac{2014}{3.4.5}+.....+\frac{2014}{2012.2013.2014}\) và N= 2013