Question

Find the sum of $7^3+8^3+9^3.....+{13}^3.$

• A. $6490$
• B. $7840$
• C. $6840$
• D. $7490$
• E. None of these

Answer 1

Answer: (B)

$7840$

Sum of $7^3+8^3+9^3+....+{13}^3$

$=1^3+2^3+3^3+...{.13}^3-(1^3+2^3...{.6}^3)$

$={\left(\frac{13(13+1)}{2}\right)}^2-{\left(\frac{6(6+1)}{2}\right)}^2$

$={\left(\frac{13\times 14}{2}\right)}^2-{\left(\frac{6\times 7}{2}\right)}^2$

$=(13\times 7{)}^2-(3\times 7{)}^2=7^2({13}^2-3^2)$

$=49\times (169-9)=49\times 160$

$=7840$ .