# Which is larger $$(1.01)^{1000000}$$ or 10,000?

## Solution :

We have, $$(1.01)^{1000000}$$  – 10000

= $$(1 + 0.01)^{1000000}$$ – 10000

By using binomial theorem,

= $$^{1000000}C_0$$ + $$^{1000000}C_1 (0.01)$$  + $$^{1000000}C_2 (0.01)^2$$  + …… + $$^{1000000}C_{1000000} (0.01)^{1000000}$$ – 10000

= (1 + 1000000(0.01) + other positive terms) – 10000

= (1 + 10000 + other positive terms) – 10000

= 1 + other positive terms > 0

Hence,  $$(1.01)^{1000000}$$ is greater than 10000.

### Similar Questions

Find the middle term in the expansion of $$({2\over 3}x^2 – {3\over 2x})^{20}$$.

Find the 9th term in the expansion of $$({x\over a} – {3a\over x^2})^{12}$$.

Find the 10th term in the binomial expansion of $$(2x^2 + {1\over x})^{12}$$.

Find the middle term in the expansion of $$(3x – {x^3\over 6})^7$$.

By using binomial theorem, expand $$(1 + x + x^2)^3$$.