Question

Which among the following is true?

• A. $(1.01{)}^{1000000}>10000$
• B. $(1.01{)}^{1000000}<10000$
• C. $(1.01{)}^{1000000}<1000$
• D. None of the above

Answer 1

Answer: (A)

Splitting $1.01$ and using binomial theorem to write the first few terms, we have $(1.01{)}^{1000000}=(1+0.01{)}^{1000000}$ $={}^{1000000}{C}_0+{}^{1000000}{C}_1(0.01)+$ Other positive terms
$=1+1000000\times 0.01+$ Other positive terms
$=1+10000+$ Other positive terms $>10000$
Hence, $(1.01{)}^{1000000}>10000$.