Among (S1): lim n → ∞ 1/(n²)(2+4+6+ +2 n)=1 (S2): lim n → ∞ 1/(n¹⁶)(1¹⁵+2¹⁵+3¹⁵+ +n¹⁵)=1/16

(B) Both (S1) and (S2) are true

(C) Both (S1) and (S2) are false

Integral Calculus: JEE Main 2023 Mathematics question

JEE Main 2023 · 13 Apr, Morning shift · Q3297

JEE Main 202313 Apr, Morning shiftMathematicsMediumIntegral Calculus369× since 2002

Among (S1):

\lim_\limits{n \rightarrow \infty} \frac{1}{n^{2}}(2+4+6+\ldots \ldots+2 n)=1

(S2) :

\lim_\limits{n \rightarrow \infty} \frac{1}{n^{16}}\left(1^{15}+2^{15}+3^{15}+\ldots \ldots+n^{15}\right)=\frac{1}{16}