Question

$(1.2{)}^{4000}$ is larger than 800

• A. True
• B. False

Answer 1

The correct option is A

True

When we get a question like this, we try to expand using binomial theorem. If we

express 1.2 as 1 + 0.2, we can see the second term in the expansion becoming 800.

$(1.2{)}^{4000}=(1+0.2{)}^{4000}$

$(1+0.2{)}^{4000}$ = ${}^{4000}{C}_0$ + ${}^{4000}{C}_1$(0.2) + ${}^{4000}{C}_1$$(0.2{)}^2$...............

$(1+0.2{)}^{4000}$ = 1 + 4000(0.2) + ${}^{4000}{C}_1$$(0.2{)}^2$.................

$(1+0.2{)}^{4000}$ = 1 + 800 + ${}^{4000}{C}_1$$(0.2{)}^2$.........

Sum of first two terms is greater than 800 and the remaining terms are all

positive.

⇒ $(1.2{)}^{4000}$ is greater than 800.