using binomial theorem determine whch number is larger 1 2^4000 or 800 - Maths - Binomial Theorem

Question

using binomial theorem determine whch number is larger 1 2^4000
or 800?

Ankush Jain · Accepted Answer

We have,
(1 2)4000 = (1+0 2)4000
Now, expanding by binomial theorem, we get
(1+0 2) 4000 = 4000C0
(1)4000 (0 2)0 + 4000C1
(1)4000-1 (0 2)1 +
4000C2 (1)4000-2 (0 2)2
+ other terms of the expansion
= 1 + 4000 Ã— (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

using binomial theorem determine whch number is larger 1.2^4000 or 800?