From March 1st until and including September 30th contains 214 days. How many periods of at least 14 consecutive days exist within the 214 days?
March 1st until and including March 14th is one period of 14 consecutive days. March 2nd until March 15th is another period of 14consecutive days. March 1st until March 15 is period of 15 consecutive days. March 1st until September 30th is a period of 214 consecutive days, the longest possible period.
What is the number of possible combinations with the 14 consecutive days constraint?
When you experiment with a few values of the period, it’s easy to spot the pattern that follows. If we want to calculate how many groups of period $k$ can be chosen from $n$ entities, we can focus on the starting point of the group. We need atleast $k$ entities to be remaining after (and including) the starting point. So, the $\#$ possible groups is $n-k+1$. For your particular problem, you just need to evaluate the sum $$\sum_{k=14}^{214} (214-k+1)$$