_ n ( 1 4 n^2-1 + 1 4 n^2-2^2 + + 1 3 n^2 ) equal to

Step-by-step solution

aligned & _ n ( 1 4 n^2-1 + 1 4 n^2-2^2 + + 1 3 n^2 ) = & _ n 1 n [ 1 4- ( 1 n )^2 + 1 4- ( 2 n )^2 + + 1 4- ( n n )^2 ] = & _ h 0 h [ 1 4-h^2 + 1 4-(2 h)^2 + + 1 4-(n h)^2 ] = & ₀^1 d x 4-x^2 = [ ⁻¹ x 2 ]₀^1 = & ⁻¹ ( 1 2 )- ⁻¹(0)= 6 aligned