Question

Which term is greater (1, 2)⁴⁰⁰⁰ or 800?

Answer 1

(1, 2)⁴⁰⁰⁰ = (1 + 0.2)⁴⁰⁰⁰ 

Now, expanding by binomial theorem, we get 

(1 + 0.2)⁴⁰⁰⁰ = ⁴⁰⁰⁰ C₀ (1)⁴⁰⁰⁰  (0.2)⁰ + ⁴⁰⁰⁰ C₁ (1^{4000  – 1} (0.2)^{1 +4000} C₃ (1)^{4000 – 3} (0.2)3 + …

 = 1 + 4000(0.2) + other terms of the expansion 

= 1 + 800 + other terms of the expansion 

= 801 + other terms of the expansion 

Hence, (1, 2)⁴⁰⁰⁰  > 800