I love being inspired! 6
Calculus
Level
5
\[\dfrac{1^2\times2^2}{10}+\dfrac{2^2\times3^2}{10^2}+\dfrac{3^2\times4^2}{10^3}+\dfrac{4^2\times5^2}{10^4}+\cdots\]
If the value of the series above is equal to \( \dfrac AB\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).
if you think the series does not converge, submit your answer as 2016.
by
Akshay Yadav