Question

Using the Binomial theorem indicate which number is larger (1−1)10000 or 1000

Answer 1

(1-1)!=1 so that (1-1)10000 is the largest than 1000

Answer 2

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