What is the parity of the sum of numbers from 1 to 200?
Answer
The sum from 1 to 200 is given by : $\begin{array}{c}1+2=\frac{2 \times 3}{2}=3 \\ 1+2+3=\frac{3 \times 4}{2}=6 \\ 1+2+3+4=\frac{4 \times 5}{2}=10 \\ \vdots \\ 1+2+3+\ldots+200=\frac{200 \times 201}{2}=20100\end{array}$
Find out the parity for the product of two (a) odd numbers and (b) even numbers.
Answer
(a) Product of two odd numbers: The parity for the product of two odd numbers is always odd. Example: 3 × 5 = 15 (odd number). (b) Product of two even numbers: The parity for the product of two even numbers is always even. Example: 4 × 6 = 24 (even number).