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Find a formula for the sum of the $n$ terms of the sequence:

$1, 1 + 2, 1 + 2 + 2^{2}, 1 + 2 + 2^{2} + 2^{3}, ...$

My Approach:

When $n$ increases the sequence increases by $2^{n}$ for every $n$.

I believe the formula has a constant which is $1$ based on the sequence pattern.

When I sum up the sequence for every $n$ it is $1, 3, 7, 15, ...$

I believe it is an arithmetic progression where $a = 1$ and $a(n) = 2a(n-1) + 3$

Although the formula is not quite correct i got some of the correct answers but not all

for every $n$.

Any help or hints would be appreciated for this

Przemysław Scherwentke
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geforce
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    (Note: I'm voting to close as abstract duplicate: the other question asks about finite sums as well. This is the case $x=2$.) – apnorton Nov 07 '14 at 23:07
  • Thanks for pointing that out anorton I can't believe I didnt see that – geforce Nov 07 '14 at 23:14

1 Answers1

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HINT: Partial sums of a geometric progression with parameters...

Przemysław Scherwentke
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