Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas JEE Main2020MathematicsDeterminantsPractice

If A r = 1 r r + 1 1 3 r 2 3 , then lim n → ∞ ⁡ ∑ r = 1 n A r is equal to

Options

  1. A0
  2. B2
  3. C4
  4. D8

Correct answer

B. 2

Step-by-step solution

A r = 1 r r + 1 1 3 r 2 3 = 1 r - 1 r + 1 1 3 r 2 3 ⇒ lim n → ∞ ⁡ ∑ r = 1 n A r = 1 - 1 2 + 1 2 - 1 3 + 1 3 - 1 4 + …     1 3 + 1 3 2 + 1 3 3 + … 2 3 = 1     1 3 1 - 1 3 2 3 = 1 1 2 2 3 = 3 - 1 = 2

Practice Determinants on Quantrex Academy →

More from Determinants

If the system of linear equations: x+y+z=6 , x+2y+5z=10 , 2x+3y+ z= has infinitely many solutions, then the value of + equals: 2026The sum of all possible values of [0, 2 ] , for which the system of equations : x 3 - 8y - 12z = 0 x 2 + 3y + 3z = 0 x + y + 3z = 0 has a non-trivial solution, is equal to : 2026If f: N Z is defined by f(n) = vmatrix n & -1 & -5 -2n^2 & 3(2k+1) & 2k+1 -3n^3 & 3k(2k+1) & 3k(k+2)+1 vmatrix , k N , and _ n=1 ^ k f(n) = 98 , then k is equal to : 2026Consider the system of linear equations in x, y, z : x + 2y + tz = 0 , 6x + y + 5tz = 0 , 3x + t^2 y + f(t) z = 0 , where f: R R is a differentiable function. If this system has in 2026If the system of equations: x+y+z=5 x+2y+3z=9 x+3y+ z= has infinitely many solutions, then the value of + is: 2026If the system of equations x + 5y + 6z = 4 , 2x + 3y + 4z = 7 , x + 6y + az = b has infinitely many solutions, then the point (a, b) lies on the line 2026Let , R be such that the system of linear equations x + 2y + z = 5 2x + y + z = 5 8x + 4y + z = 18 has no solution. Then is equal to : 2026The system of linear equations x+y+z=6 2 x+5 y+a z=36 x+2 y+3 z=b has 2026 Full Determinants list All NTA Abhyas JEE Main PYQs