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.

statement #3: proof- ang is congruent to ang ecd : angles are congruent.  

step-by-step explanation:

1: the missing angles in statement #3  

a.) acb  

reason- the reason why the answer is acb is because angle ecd and angle acb are both the same size *that's what the word congruent means this is really simple.  

2: the missing word in reason #3  

c.) vertical  

reason- the reason why the answer is vertical is because the angles in that diagram on figure 2 is slanted, which is vertical, and the e and a both lay on vertical lines. along with the other's, but e and a are the 2 main points you want to focus on. and c is kind of like your starting point, because c is for both angles, not just one.  

i hope that was and understanding.