Question

10. Using Binomial Theorem, indicate which number is larger (1.1)1000 or 1000.​

Answer 1

By splitting the given 1.1 and then applying binomial theorem, the first few terms of (1.1)¹⁰⁰⁰⁰ can be obtained as

(1.1)¹⁰⁰⁰⁰ = (1 + 0.1)¹⁰⁰⁰⁰

• = (1 + 0.1)¹⁰⁰⁰⁰ C1 (1.1) + other positive terms
• = 1 + ¹⁰⁰⁰⁰ × 1.1 + other positive terms
• = 1 + 11000 + other positive terms
• = 1000

(1.1)¹⁰⁰⁰⁰ > 1000