+31 You can evaluate it as the difference of two sums (relating problems to similar problems).
One sum is 0+2+4+6+8+...+86.
+1252 Solution: 1,710
Divide the series by two; we can multiply by 2 later.
14+15+16+...+42+43.
The formula of finding the sum of the first \(n\) positive integers is \(\frac{n \times (n+1)}{2}\).
We can first find the sum until 43, then subtract the sum until 13 to get the value of 14+15+16+...+42+43.
First plugging in 43, we get \(\frac{43 \times (43+1)}{2} = 946\).
Then plugging in 13, we get \(\frac{13 \times (13+1)}{2} = 91\).
\(946-91=855\).
We still need to multiply by 2 to get our final answer.
\(855 \times 2 = 1710\).
You are very welcome!
:P
