Mathematics

Problem

a. Write down the value of

e^2

correct to 5 s.f. &emsp; &emsp;b. Write down, correct to 5 s.f., the values of the expression

\left(1 + \frac{2}{n}\right)^n

for the values of

n

shown on the following table:

| 1 000 000 | | &emsp; &emsp;c. Hence, guess the value of

\lim_{n \to +\infty} \left(1 + \frac{2}{n}\right)^n

&emsp; &emsp;d. By following a similar rationale guess the value of

\lim_{n \to +\infty} \left(1 + \frac{3}{n}\right)^n