Question

Using Binomial Theorem, indicate which number is larger (1.1)^10000 or 1000.

Answer 1

Splitting 1.1 and using Binomial Theorem to write the first few terms we have

(1.1)¹⁰⁰⁰⁰ = (1+0.1)¹⁰⁰⁰⁰ 
              = ¹⁰⁰⁰⁰C₀ + ¹⁰⁰⁰⁰C₁(0.1) +¹⁰⁰⁰⁰C₂(0.1)² + other positive terms.
              = 1 + 10000 ´ (0.1) + other positive terms
              = 1 + 1000 + other positive terms
              >1000
Hence, (1.1)¹⁰⁰⁰⁰ > 1000.