Question

an exponential sequence (geometric progression) has first term x and common ratio x ,x≠1 write down the sum of the first n terms of this sequence


(1a): write down the sum of the first n terms of this sequence

(1b): |x|<1 find lim Sn as n=>infinity

(1c): if An=sum r=1 to n Sr,show that
(1-x)An=nx-xSn

Please help me show working this one difficult for me

Answer 1

as with any geometric sequence,
Sn = a(1-r^n)/(1-r)
So, since a=x and r=x,
Sn = x(1-x^n)/(1-x)

1b) S = a/(1-r) = x/(1-x)

1c should not be too hard now.