Question

The value of $(1.02{)}^4+(0.98{)}^4$ correct to three decimal places is

• A. $2.004$
• B. $2.005$
• C. $2.006$
• D. $1.995$

Answer 1

Answer: (B)

$2.005$

$(1.02{)}^4+(0.98{)}^4$
$=(1+0.02{)}^4+(1-0.02{)}^4$
All the even terms at even positions would be eliminated and we would be left with.
$2(1+{}^4{C}_2(0.02{)}^2+{}^4{C}_4\left(0.02{)}^4\right)$
$=2(1+6(4\left)\right({10}^{-4})$
Higher terms can be neglected, as they would yield a value greater than $3$ decimal places.
Hence, $2(1+(0.0024)$
$=2\left(1.0024\right)$
$=2.0048$
By rounding off we get $2.005$.