Question

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

• A. 4
• B. 5
• C. 2
• D. 3

Answer 1

Answer: (D)

3

Answer 2

We know that $- \frac{3}{8}x^{2}(1 - x)^{- 1/2}$ and $- \frac{3}{8}x^{2}\left( 1 + \frac{x}{2} + .... \right)$.

∴ $- \frac{3}{8}x^{2}$ (By putting n = 10000)

Also $nC_{r}$

$nC_{r + 1}$upto10001 terms

$\Rightarrow \frac{n!}{(n - r)!r!} = \frac{n!}{(n - r - 1)!(r + 1)!}$. Hence 3 is the positive integer just greater than $\Rightarrow \frac{1}{(n - r)(n - r - 1)!r!} = \frac{1}{(n - r - 1)!(r + 1)r!}$.

Hence (4) is the correct option.