what is the summation from i=0 to log(n)

Question

I need to know how to get the summation of a constant (c) from i=0 to log(n) of a constant

Answer 1

$$\sum_{i = 0}^{\ln(n)} C = C \sum_{i = 0}^{\ln(n)} 1 = C\cdot (\ln(n)+1) = C\ln(n) + C $$

"More rigorously"

$$\lim_{N\to \ln(n)} \sum_{i = 0}^{N} C = C\cdot (N+1) = C\ln(n) + C$$