∑n=652(7n+1)
Solution
The given expression is a sum of an arithmetic sequence (also known as an arithmetic series). The general form of an arithmetic sequence is a + (n-1)d, where a is the first term, d is the common difference, and n is the term number.
In this case, the first term a = 7*65 + 1 = 456, the common difference d = 7, and the number of terms n = 52.
The sum S of the first n terms of an arithmetic sequence can be found using the formula S = n/2 * (a + l), where l is the last term.
First, we need to find the last term l. We can use the formula for the nth term of an arithmetic sequence, which is l = a + (n-1)d. Substituting the given values, we get l = 456 + (52-1)*7 = 812.
Now we can find the sum S. Substituting the given values into the formula, we get S = 52/2 * (456 + 812) = 26 * 1268 = 32968.
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