Which answer represents the series in sigma notation?

  see below

Step-by-step explanation:

Try j=1 and j=2 in each of the series expressions to see which ones work.

A: 1/3(1+1) = 2/3 ≠ 1 . . . . first term doesn't match

B: 3^(1-1) = 3^0 = 1 . . . . first term matches;

  3^(2-1) = 3^1 = 3 ≠ 1/3 . . . . .second term doesn't match

C: (1/3)^(1-1) = 1 . . . . . . . first term matches

   (1/3)^(2-1) = (1/3)^1 = 1/3 . . . second term matches

D: (1/3)(1) +1 = 4/3 ≠ 1 . . . . . first term doesn't match

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The third choice is a summation that matches the given series expression.

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