Let us have a look at this series:

```
nm + (n-1)(m-1) + (n-2)(m-2) + (n-3)(m-3) + ...... + (until either n==1 or m==1).
```

**Example:**

Let, n=5, m=3. So we need to find the summation of

```
5.3 + 4.2 + 3.1
```

Well, what I need is a closed form. And how should I find out a closed form of such kind of series?

Thanks in advance! :)

let's assume that n < m

we know that 1*1 + 2*2 + 3*3 + ... + k*k = (2k + 1)(k + 1)k / 6

so we just need to calculate (m — n)*n + (m — n) * (n-1) + ... which is equal to (m — n) * (n + 1)n/2

so it will be (2n+1)(n+1)n/6 + (m-n)(n+1)n/2 = ((n+1)(n)(3m — n + 1))/6

Okay I got it. Tricky and beautiful.

PS: Did you participate Codechef's Kodeathon? You are so fast! :)

No i didn't and thanks :D

Let's suppose that

n≤m.S=n^{2}·m- (n+m)n(n- 1) / 2 + (n- 1)n(2n- 1) / 6Thank you!

14 revisions ? I love your dedication to help