First slide

Introduction to limits

Question

$lim_{n \to \infty} \frac{1 + 2 + 3 + \dots + n}{1 + 3 + 5 + \dots + (2 n - 1)} =$

Moderate

A

1
B

3/2
C

$\frac{1}{2}$
D

2

Solution

We have,
$\begin{array}{l} lim_{n \to \infty} \frac{1 + 2 + 3 + \dots + n}{1 + 3 + 5 + \dots + (2 n - 1)} = lim_{n \to \infty} \frac{\frac{n (n + 1)}{2}}{n^{2}} \\ = lim_{n \to \infty} \frac{n (n + 1)}{2 n^{2}} = lim_{n \to \infty} \frac{n^{2} + n}{2 n^{2}} = \frac{1}{2} \end{array}$

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