( _ r=1 ^ n (2 r-1)=x ) then ( _ n [ 1³ x² + 2³ x² + 3³ ² + + n³ ² ]= )

Step-by-step solution

( ( A ) ) ( x=1+3+5+ +(2 n-1) ) ( x=n² ) ( x²=n⁴ ) ( _ n [ 1³+2³+ +n³ x² ] ) ( _ n [ n²(n+1)² 4 n⁴ ] ) ( _ n [ n² n² (1+ 1 n )² 4 n⁴ ] ) ( _ n [ (1+ 1 n )² 4 ]= 1 4 )