Given the series 2 two-thirds startfraction 4 over 9 endfraction startfraction 8 over 27 endfraction startfraction 16 over 81 endfraction startfraction 32 over 243 endfraction ellipsis, which partial sums are correct? check all that apply. s1 = 2 s2 = 4 s subscript 3 = startfraction 28 over 9 endfraction s subscript 4 = startfraction 10 over 9 endfraction s subscript 6 = startfraction 292 over 81 endfraction

A partial sum (simply put) refers to the sum of the various parts that make up a sequence.
One of a series of sums of elements of a given sequence, the first sum being the first element, the second sum being the first element added to the second element, the third sum being equal to the sum of the first three elements, and so on.
A partial sum of an infinite series is the sum of a finite number of consecutive terms beginning with the first term.
When working with infinite series, it is often helpful to examine the behavior of the partial sums.

A partial sum would be:

2 + (2/3).

In this case, thus,

Series 1 = 2 - This is correct.

Series 2 = 2 + (2/3) = 8/3 - incorrect

Series 3 = (8/3) + (4/9) = (28/9) Correct

Series 4 = (28/9) + (8/27) = (92/27)

Series 5 = (92/27) + (16/81) = 292/81

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