Question

Which of the following values is closest to k when k=(1+\frac{1}{n})^n, given n is equal to the number of seconds in one year?

Answer 1

k is closest to e

Step-by-step explanation:

Given

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

Where n is the number of seconds in one year

Number of seconds in a year

$=365\times 24\times 60\times 60$

$=32061600$

Thus,

$k=(1+\frac{1}{32061600})^{32061600}$

We know that

$\lim_{n \to \infty} (n+\frac{1}{n})^n=e$

Since 32061600 is sufficiently large number

Therefore, we can say that

$k\approx e$

or $k\approx 2.72$

Hope this answer is helpful.

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