Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2016MathematicsLimits

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

Options

  1. A1 3
  2. B- 1 3
  3. C1 6
  4. D- 1 6

Correct answer

B. - 1 3

Step-by-step solution

_ n 1 1-n^3 _ r=1 ^n r^2= _ n 1 n^3 ( 1 n^3 -1 ) n(n+1)(2 n+1) 6 = _ n n^3 (1+ 1 n ) (2+ 1 n ) n^3 ( 1 n^3 -1 ) 6 =- 1 3

Practice Limits on Quantrex Academy →

More from Limits

If _ x 0 ( p 2x + 1 - 2x x + x ) = 1 then the value of ' p ' is 2026_ x 2 ( 1 - x x ) is equal to 2026The value of _ x 3 [ 1 x-3 + 9x 27-x^3 ] is: 2026_ x 0 (1 - 2x)(3 + x) x 4x is equal to: 2026If _ x 3 ( x^2 - ax - 3b x - 3 ) = 5 , then a + b = 2026If f(x) = cases x^2 - 1 & if x 2 x + 1 & if x < 2 cases , then _ x 1 f(x) + _ x 2 f(x) = 2026_ x 4 2 2 -( x+ x)^3 1- 2 x = 2025Let [x] denote the greatest integer less than or equal to x . Then _ x 2⁺ ( [x]^3 3 - [ x 3 ]^3 )= 2025 Full Limits list All Manipal MET PYQs