SOLUTION: What is the formula for: 1+(1+2)+(1+2+3+4)+(1+2+3+4+5+6+7+8)+... and how is it derived? I do know the formula btw (-: but I am not sure how to derive it.

Question 877695: What is the formula for:
1+(1+2)+(1+2+3+4)+(1+2+3+4+5+6+7+8)+...
and how is it derived? I do know the formula btw (-: but I am not sure how to derive it.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Recall 1+2+...+n = n(n+1)/2. If we can find a general formula for

, we are essentially done.

Rewrite as

. The latter term is equal to

. Note that the first sum is geometric with common ratio 4 (can be written as 1^2 + 4^2 + ... + 4^n) and is equal to

.

Therefore the sum is

, which I'll leave you to simplify.
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