KCET2024MathematicsLimits
_ n ( n n^2+1^2 + n n^2+2^2 + n n^2+3^2 + + 1 5 n )=
Options
- A/ 4
- B⁻¹ 3
- C⁻¹ 2
- D/ 2
Correct answer
C. ⁻¹ 2
Step-by-step solution
_ n ( n n^2+1^2 + n n^2+2^2 + n n^2+3^2 + + 1 5 n )= _ n ( n n^2+1^2 + n n^2+2^2 + n n^2+3^2 + + n n^2+(2 n)^2 )= _ n _ r=1 ^ 2 n n n^2+r^2 = _ n _ r=1 ^ 2 n 1 n ( 1 1+ ( r n )^2 )= ₀^2 d x 1+x^2 = ⁻¹(2)