Which one of the following is true?

Question

Which one of the following is true? (A) (1+(1/n))n < n2 , n is positive integer (B) (1+(1/n))n < 2 , n is positive integer (C) (1+(1/n))n < n3 , n is positive integer (D) (1+(1/n))n ge 2 , n is positive integer

Tardigrade Admin · Accepted Answer

All except (d) are not true for n = 1.

Q. Which one of the following is true?

$(1 + \frac{1}{n})^{n} < n^{2}, n$ is positive integer

$(1 + \frac{1}{n})^{n} < 2, n$ is positive integer

$(1 + \frac{1}{n})^{n} < n^{3}, n$ is positive integer

$(1 + \frac{1}{n})^{n} \geq 2, n$ is positive integer

All except $(d)$ are not true for $n = 1$ .

Q. Which one of the following is true?

(1+n1​)n<n2,n is positive integer

(1+n1​)n<2,n is positive integer

(1+n1​)n<n3,n is positive integer

(1+n1​)n≥2,n is positive integer

All except (d) are not true for n=1.

$(1 + \frac{1}{n})^{n} < n^{2}, n$ is positive integer

$(1 + \frac{1}{n})^{n} < 2, n$ is positive integer

$(1 + \frac{1}{n})^{n} < n^{3}, n$ is positive integer

$(1 + \frac{1}{n})^{n} \geq 2, n$ is positive integer

All except $(d)$ are not true for $n = 1$ .