Final answer:
To express the given sum in summation notation, use the arithmetic series formula. The formula is S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term. Apply this formula to the given sum by plugging in the corresponding values.
Step-by-step explanation:
The given expression represents a sum of terms with alternating signs, where the signs also alternate for the exponents of 7. To express this sum using summation notation, we can use the formula for an arithmetic series. The general formula for an arithmetic series is S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term.
In this case, the first term is 1, the number of terms is 10, and the last term is (-1)^(9)((1)/(7^(9))). Therefore, the sum can be expressed as:
S = (10/2)(1 + (-1)^(9)((1)/(7^(9))))