Supplementary Material

Find the sum to infinity in each of the following Geometric Progression. $1, \frac{1}{3}, \frac{1}{9}, \ldots$

Find the sum to infinity in each of the following Geometric Progression. $6, 1.2, .24, \ldots$

Find the sum to infinity in each of the following Geometric Progression. $5, \frac{20}{7}, \frac{80}{49}, \ldots$

Find the sum to infinity in each of the following Geometric Progression. $\frac{-3}{4}, \frac{3}{16}, \frac{-3}{64}, \ldots$

Prove that $3^{\frac{1}{2}} \times 3^{\frac{1}{4}} \times 3^{\frac{1}{8}} \ldots = 3$

Let $x = 1 + a + a^2 + \ldots$ and $y = 1 + b + b^2 + \ldots$, where $|a| < 1$ and $|b| < 1$. Prove that

Evaluate the following limit, if exist: $\lim_{x \to 0} \frac{e^{4x} - 1}{x}$

Evaluate the following limit, if exist: $\lim_{x \to 0} \frac{e^{2+x} - e^2}{x}$

Evaluate the following limit, if exist: $\lim_{x \to 5} \frac{e^x - e^5}{x - 5}$

Evaluate the following limit, if exist: $\lim_{x \to 0} \frac{e^{\sin x} - 1}{x}$

Evaluate the following limit, if exist: $\lim_{x \to 3} \frac{e^x - e^3}{x - 3}$

Evaluate the following limit, if exist: $\lim_{x \to 0} \frac{x(e^x - 1)}{1 - \cos x}$

Evaluate the following limit, if exist: $\lim_{x \to 0} \frac{\log_e (1 + 2x)}{x}$

Evaluate the following limit, if exist: $\lim_{x \to 0} \frac{\log (1 + x^3)}{\sin^3 x}$