Question

${11}^3+{12}^3+{13}^3+...+{20}^3=$

• A. 45650
• B. 47125
• C. 44100
• D. 41075

Answer 1

The correct option is D 41075

Note that ${11}^3+{12}^3+{13}^3+...+{20}^3=[1^3+2^3+...+{20}^3]-[1^3+2^3+...+{10}^3].$

The sum of cubes of first $n$ natural numbers is given by
$S_n=[\frac{n(n+1)}{2}{]}^2.$

$\Rightarrow 1^3+2^3+...+{20}^3=[\frac{20(20+1)}{2}{]}^2=44100$
Similarly, $1^3+2^3+...+{10}^3=[\frac{10(10+1)}{2}{]}^2=3025.$
$\therefore {11}^3+{12}^3+{13}^3+...+{20}^3=44100-3025=41075$