lim n → ∞ 3 n 4 + 2 + 1 n 2 + 2 + 2 n 2 + … + 3 - 1 n 2 is equal to

limn→∞3n4+2+1n2+2+2n2+…+3-1n2 is equal to
  1. 12
  2. 193
  3. 0
  4. 19

Solution

Let

L=limn→∞3n4+2+1n2+2+2n2+...+3-1n2

⇒L=limn→∞3n2+0n2+2+1n2+2+2n2+...+2+1-1n2

⇒L=3limn→∞1n∑r=0n-12+rn2

⇒L=3∫012+x2dx

⇒L=2+x301

⇒L=27-8

⇒L=19

Asked in: JEE Main 2023 (30 Jan Shift 2)

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