Question

Find the last digit of the number $1^3+2^3+3^3+4^3\cdots +{99}^3$.

• A. 1
• B. 2
• C. 5

Answer 1

The required units digit would be given by the series:
(1 + 8 + 7 + 4 + 5 + 6 + 3 + 2 + 9 + 0) repeated 10 times (since the units digit of ${11}^3+{12}^3\cdots +{19}^3+{20}^3$ would be the same as the unit digit of $1^3+2^3+3^3+4^3\cdots +9^3+{10}^3$). Hence, the required unit digit would be 0.