Question

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

• A. 1
• B. 2
• C. 3

Answer 1

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