Find S15 for the geometric series 72 + 12 + 2 + +…
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1) , and
. Subtracting this from the numerator gives a remainder of
, and
. Subtracting this from the previous remainder gives a new remainder of
This means that
2) , and
. Subtracting this from the numerator gives a remainder of
, and
. Subtracting this from the previous remainder gives a new remainder of
, and
. Subtracting this from the previous remainder gives a new remainder of
This means that
3) will be a factor of
if dividing the latter by
leaves a remainder of 0.
, and
. Subtracting this from the numerator gives a remainder of
, and
. Subtracting this from the previous remainder gives a new remainder of
, and
. Subtracting this from the previous remainder gives a new remainder of
and since the remainder is 0, is indeed a factor of
.