Question

10,000 is larger than $(1.01{)}^{1000000}$

• A. True
• B. False

Answer 1

The correct option is B

False

This is similar to the previous problem. We will proceed the same way.

$(1.01{)}^{1000000}=(1+0.01{)}^{1000000}$

$(1+0.01{)}^{1000000}$ = ${}^{1000000}{C}_0$ + ${}^{1000000}{C}_1$$(0.01{)}^1$ + ${}^{1000000}{C}_2$$(0.01{)}^2$...........

$(1+0.01{)}^{1000000}$ = 1 + 1000000$(0.01{)}^1$ + ${}^{1000000}{C}_2$$(0.01{)}^2$.....................

$(1+0.01{)}^{1000000}$ = 1 + 1000000 + ${}^{1000000}{C}_2$$(0.01{)}^2$.................

Sum of first two terms is greater than 10,000 and the remaining terms are all

positive.

⇒ $(1.01{)}^{1000000}$ is greater than 10,000.