Question

n! = 1.2.3.4.....n (\(n\in N\)*; n\(\ge\)2)

Chứng minh \(\dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+......+\dfrac{2013}{2014!}< 1\)

Answer 1

Từ đề có:

\(\dfrac{2-1}{2!}\) + \(\dfrac{3-1}{3!}\) + .... + \(\dfrac{2014-1}{2014!}\)

= \(\dfrac{2}{2!}\) - \(\dfrac{1}{2!}\) + \(\dfrac{3}{3!}\) - \(\dfrac{1}{3!}\) + .... + \(\dfrac{2014}{2014!}\) - \(\dfrac{1}{2014!}\)

= 1 - \(\dfrac{1}{2!}\) + \(\dfrac{1}{2!}\) - \(\dfrac{1}{3!}\) + .... + \(\dfrac{1}{2013!}\) - \(\dfrac{1}{2014!}\)

= 1 - \(\dfrac{1}{2014!}\), rứa đủ rồi đúng không ?

Có chi không hiểu mai ta giảng cho nhớ tick đúng nha

Answer 2

=))

Answer 3