Let's say Un=aqn and Sn=a+aq+aq2+aq3+aq4+aq5+...+aqn
Sn = a (1+q+q2+q3+q4+q5+...+qn)
A=(Sn/a) - q (Sn/a) = (1+q+q2+q3+q4+q5+...+qn) - q(1+q+q2+q3+q4+q5+...+qn)
A=1+q+q2+q3+q4+q5+...+qn-q-q2-q3-....-qn-qn+1=1-qn+1
So A = 1-qn+1 = Sn/a (1-q)
So Sn = a (1-qn+1)/(1-q)
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It depends on the series.
The sum of the series a + ar + ar2 + ... is a/(1 - r) for |r| < 1
1/8
The geometric sequence with three terms with a sum of nine and the sum to infinity of 8 is -9,-18, and 36. The first term is -9 and the common ratio is -2.
No.