Math Formula Sheet

Mathematical analysis → Limits

MR-830 / 830.

$\underset{n \to \infty}{l i m} {(1 + \frac{2}{n + 1})}^{n}$

MR-831 / 831.

$\underset{n \to \infty}{l i m} \frac{n + 3}{n^{2} + 3 n + 2}$

MR-832 / 1503.

Determine the limit value of the series:

$a_{n} = {(1 + \frac{3}{n})}^{n}$

MR-833 / 1512.

The sum of the first n terms of the series:

$S_{n} = \frac{5^{n + 1} - 5}{4 \cdot 5^{n}}$

a) Determine the general term of the series and check if it is convergent!

b) Determine the sum of the sequence when the number of members increases indefinitely!

$\underset{n \to \infty}{l i m} S_{n}$

MR-834 / 1513.

The sum of the first n terms of the series:

$S_{n} = \frac{2^{n + 2} - 4}{2^{n}}$

a) Determine the general term of the series and the limiting value of the series!

b) Determine the sum of the sequence when the number of members increases indefinitely!

$\underset{n \to \infty}{l i m} S_{n}$