# Math Help - Negative Binomial

1. ## Negative Binomial

When I try solving the attached problem, I do not get the same answer in my book which is 0.5580.

Since the problem is at most 20, I have done the following:

0.04(0.96^0 + 0.96^1 + 0.96^2 + 0.96^3 + 0.96^4 + ... + 0.96^19) = 0.535243

Any suggestions in going about this problem would be helpful!

2. Originally Posted by MathRules!
When I try solving the attached problem, I do not get the same answer in my book which is 0.5580.

Since the problem is at most 20, I have done the following:

0.04(0.96^0 + 0.96^1 + 0.96^2 + 0.96^3 + 0.96^4 + ... + 0.96^19) Mr F says: This is correct.

= 0.535243 Mr F says: This is wrong.

Any suggestions in going about this problem would be helpful!
It looks like you haven't correctly used the formula for the sum of a geometric series.

The answer is $(0.04) \left( \frac{(0.96)^{20} - 1}{0.96 - 1}\right)$.