SEAMO X 2022 — Paper D — Grade 7–8 Question 1

Let $A=\sum_{k=1}^{2022}\frac1{k\sqrt{k+1}+(k+1)\sqrt k}$. Suppose $A=a+b/\sqrt c$, with integers a,b,c and c divisible by no perfect square greater than one. Find a+b+c.