Find the sum of the summation notation if the upper limit is 50, k=1 and (3k+2)
To find the sum of the summation notation with an upper limit of 50, where k starts at 1 and the function inside the summation notation is (3k+2), we need to find:
(3(1) + 2) + (3(2) + 2) + (3(3) + 2) + ... + (3(50) + 2)
= 5 + 8 + 11 + ... + 152
To find the sum of this arithmetic series, we can use the formula for the sum of the first n terms of an arithmetic sequence:
Sum = n/2 * (first term + last term)
In this case, n = 50, the first term = 5, and the last term = 152. Plugging these values into the formula:
Sum = 50/2 * (5 + 152)
Sum = 25 * 157
Sum = 3925
Therefore, the sum of the summation notation with k starting at 1, the upper limit being 50, and the function (3k+2) is 3925.