Definite Integration Question 15
Question 15 - 30 January - Shift 2
So, it is true for every natural no. ‘$n$’
$\lim _{n \to \infty} \frac{3}{n}{4+(2+\frac{1}{n})^{2}+(2+\frac{2}{n})^{2}+\ldots+(3-\frac{1}{n})^{2}}$
is equal to
(1) 12
(2) $\frac{19}{3}$
(3) 0
(4) 19
Show Answer
Answer: (4)
Solution:
Formula: Definite integrals as a limit of sum, Standard formulas for Indefinite Integration
$L=\lim _{n \to \infty} \frac{3}{n} \sum _{r=0}^{n-1}(2+\frac{r}{n})^{2}$
$L=3 \int_0^{1}(2+x)^{2} dx=27-8=19$
