Probabilities question

1. Mar 28, 2013

cdux

That's not exactly coursework (it's studying) but I've spammed the probabilities forum too much.

Can someone explain this part?

Knowing that P(k)=P(X=k)=c(101-k)

For a 'turtle' that can live up to 100 years, find 'c'.

And it goes

I don't understand the jump from cΣk to c100(100+1)/2

2. Mar 28, 2013

Staff: Mentor

$$\sum_{k=1}^n k = (1+n) \frac{n}{2}$$
To see how to get the formula, list the numbers of the sum, then sum the first with the last, the second with the second to last, etc.

3. Mar 28, 2013

cdux

Ah, hacky. I was expecting a more straightforward way.

Thank you!