Question

a=81+2*81+3*81+...+49*81

Answer 1

$A=81(1+2+3+...+49)= \\ \\ ~~~=81 \cdot \frac{49 \cdot 50}{2}= \\ \\ ~~~=81 \cdot 49 \cdot 25= \\ \\ ~~~=9^2 \cdot 7^2 \cdot 5^2= \\ \\ ~~~= \boxed{ (5 \cdot 7 \cdot 9)^2}-patrat~perfect$

Answer 2

A=81*(1+2+3+...+49)=81* $\frac{49\cdot50}{2}$
A=81 * 49 * 25 = (5*7*9)² = 315² =99225;