Prove that:
B = \(\dfrac{1}{2!}+\dfrac{5}{3!}+\dfrac{11}{4!}+...+\dfrac{n^2+n-1}{\left(n+1\right)!}< 2\).
Help me please! This is my homework and I must give it to my teacher tomorrow!
\(\dfrac{3}{4}+\dfrac{5}{36}+\dfrac{7}{144}+...+\dfrac{2n+1}{n^2\left(n+1\right)^2}< 1\)(n \(\in\)N*)
Prove that \(\dfrac{1}{2^3}+\dfrac{1}{3^3}+\dfrac{1}{4^3}+...+\dfrac{1}{n^3}< \dfrac{1}{4}\left(n\in N;n\ge2\right)\)
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Prove that E = \(\dfrac{1}{3^3}+\dfrac{1}{4^3}+\dfrac{1}{5^3}+...+\dfrac{1}{n^3}< \dfrac{1}{12}\).
Given natural numbers, a and b, that sastify the expression: (a + 2016b) \(⋮\) 2017. Prove that:
A = (2a + 2015b)(3a + 2014b)...(2015a + 2b) \(⋮\) 20172014.