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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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