To evaluate the summation of the expression 2n + 5 from n = 1 to n = 12, we can break it down into two separate summations.
First, we calculate the summation of 2n:
- The summation of n from 1 to 12 is given by the formula: Σn = n(n + 1)/2. Thus, for n = 12, we have:
- Σn = 12(12 + 1)/2 = 12(13)/2 = 78.
- Now, since we have 2n, we multiply this result by 2:
- Σ(2n) = 2 * 78 = 156.
Next, we calculate the summation of the constant 5 over 12 terms:
- Since we are adding 5 a total of 12 times, the result is:
- Σ5 = 5 * 12 = 60.
Now, we add the results of the two summations together:
- Total = Σ(2n) + Σ5 = 156 + 60 = 216.
Therefore, the evaluation of the summation of 2n + 5 from n = 1 to n = 12 is 216.