R Programming Perform negative binomial distribution

Question

I want to know why I am getting a different answer while using density function in R:

pnbinom(3,2,.5)
#[1] 0.8125

a=dnbinom(5,0,0.5)+dnbinom(4,1,.5)+dnbinom(3,2,.5)
a
#[1] 0.15625

Answer 1

Try this:

pnbinom(3,2,0.5)

sum(dnbinom(0:3,2,0.5))

This will give the following output:

> pnbinom(3,2,0.5)
[1] 0.8125
> 
> sum(dnbinom(0:3,2,0.5))
[1] 0.8125