Question

The positive integer just greater than (1 + 0.0001)¹⁰⁰⁰⁰ is ______.

विकल्प

• 4

• 5

• 2

• 3

Answer 1

The positive integer just greater than (1 + 0.0001)¹⁰⁰⁰⁰ is 3.

Explanation:

(1 + 0.0001)¹⁰⁰⁰⁰ = `(1 + 1/n)^n`, n = 10000

= `1 + n. 1/n + (n(n - 1))/(2!) 1/n^2 + (n(n - 1)(n - 2))/(3!) 1/n^3 + ... + 1/n^n`

= `1 + 1 + 1/(2!)(1 - 1/n) + 1/(3!)(1 - 1/n)(1 - 2/n) + ... + 1/n^n < 1 + 1/(1!) + 1/(2!) + 1/(3!) + ........ + 1/((9999)!)`

= `1 + 1/(1!) + 1/(2!) + ....... ∞`

= e < 3