# Sum of even numbers from n to m regardless if nm JavaScript

We are required to write a function that takes two numbers as arguments m and n, and it returns the sum of all even numbers that falls between m and n (both inclusive)

For example −

If m = 10 and n = -4

The output should be 10+8+6+4+2+0+(-2)+(-4) = 24

## Approach

We will first calculate the sum of all even numbers up to n and the sum of all even numbers up to m.

Then we will check for the bigger of the two m and n. Subtract the sum of smaller from the sum of bigger which will eventually give us the sum between m and n.

## Formula

Sum of all even number from 0 to N is given by −

$$\frac{N\times(N+2)}{4}$$

Therefore, let’s put all this into code −

## Example

const sumEven = n => (n*(n+2))/4;
const evenSumBetween = (a, b) => {
return a > b ? sumEven(a) - sumEven(b) + b : sumEven(b) - sumEven(a) + a;
};
console.log(evenSumBetween(-4, 10));
console.log(evenSumBetween(4, 16));
console.log(evenSumBetween(0, 10));
console.log(evenSumBetween(8, 8));
console.log(evenSumBetween(-4, 4));

## Output

The output in the console will be −

24
70
30
8
0

Updated on: 24-Aug-2020

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