Algebra-30 (NCERT)

Which is larger (1.01)^1000000 or 10000?

Solution follows here:

Solution:

This is a straight forward question on Binomial expansion.

(x+y)ⁿ = nC0 xⁿ y⁰ + nC1 x^n-1 y¹ + nC2 x^n-2 y² + . + ncn x⁰ yⁿ

(1.01)^1000000 
= (1000000)C0 + (1000000)C1 (0.01)¹ + (1000000)C2 (0.01)² +…. + (0.01) ^1000000

= 1 + (1000000)(0.01) + …..

= 1+ 10000 + …

> 10000

Hence (1.01)^1000000 is greater than 10000