Question

The approximation of $(0.99{)}^5$ using the first three terms of its expansion is

• A. $0.851$
• B. $0.751$
• C. $0.951$
• D. None of these

Answer 1

Answer: (C)

Now, $(0.99{)}^5=(1-0.01{)}^5$
$={}^5{C}_0(1{)}^5-{}^5{C}_1(1{)}^4(0.01)+{}^5{C}_2(1{)}^3(0.01{)}^2$
(ignore the other terms)
$=1-5\times 1\times 0.01+\frac{5\times 4}{2}\times 1\times 0.01\times 0.01$
$=1-0.05+10\times 0.0001=1-0.05+0.001$
$=1.001-0.05=0.951$