Find the following sums : (i) ` 12 + 13 + 14 + …+ 37` (ii) ` 18^(2) + 19^(2) + 20 ^(2) +…+ 47^(2)` (iii)` 2^(3) + 4^(3) + 6^(3) +… + 18^(3) `

Explanation

Let's solve the given sums step by step.

### (i) Find the sum: `12 + 13 + 14 + … + 37`

1. **Identify the series**: The series is an arithmetic series where the first term \( a = 12 \) and the last term \( l = 37 \).
2. **Find the number of terms (n)**:
\[
n = \frac{l - a}{d} + 1
...