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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

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1 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.

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    oobleck

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