Prove that:
\(\dfrac{9}{10!}+\dfrac{9}{11!}+...+\dfrac{9}{1000!}< \dfrac{1}{9!}\)
Calculate:
\(\dfrac{1}{1.2.3.4}+\dfrac{1}{2.3.4.5}+...+\dfrac{1}{17.18.19.20}\).
Compact:
\(\dfrac{1.2+2.4+3.6}{2.4+4.8+6.12}\)
\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+...+\dfrac{1}{2017^2}\)< \(1\)