Answer:
Option B.
Step-by-step explanation:
Each summation symbol tells you to add terms. The terms are obtained by replacing n in the expression with the integers 1, 2, 3, 4, 5, and 6.
Let's look at option A:
The expression is 2(2)^n.
Replacing n with 1, 2, ..., 6 gives us these terms, which are added:
2(2)^1, 2(2)^2, 2(2)^3, 2(2)^4, 2(2)^5, 2(2)^6
The terms above simplify to:
4, 8, 16, 32, 64, 128
Clearly these are not the terms in the series you are given, so option A is not the answer.
Let's now look at option B:
Replacing n in 2n with 1, 2, 3, ..., 6 gives us:
2(1), 2(2), 2(3), 2(4), 2(5), 2(6) which simplifies to 2, 4, 6, 8, 10, 12.
Since it's a summation, you add the terms above to get
2 + 4 + 6 + 8 + 10 + 12
Option B is the answer.
