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Please refer to the attached sheet.
I need help with part b)
for part
a)
I did:
$\sum\limits_{n=0}^{\infty} a^n = \frac{1}{1a}$
So for
$\sum\limits_{x=0}^{\infty} a^{2x}$
$a^{2x} = (a^2)^x$
and
$\sum\limits_{x=0}^{\infty} (a^2)^x = \frac{1}{1a^2}$
for part b)
the solutions say i am wrong.
I did this:
$c$ $\sum\limits_{n=0}^{\infty} a^n = \frac{c}{1a} = 1$
therefore
$c = 1a^2$ (from part a)
The answer is not this. Solutions are:
$\sum\limits_{x=1}^{\infty} c(a^2)^x = 1$
$ ...$
$c = \frac{a^{2x}(1a^2)}{a^2}$
Why do we begin from $x=1$ and not $x=0$ when summing this series? Is this always the case for these questions? How do I solve part b?
I need help with part b)
for part
a)
I did:
$\sum\limits_{n=0}^{\infty} a^n = \frac{1}{1a}$
So for
$\sum\limits_{x=0}^{\infty} a^{2x}$
$a^{2x} = (a^2)^x$
and
$\sum\limits_{x=0}^{\infty} (a^2)^x = \frac{1}{1a^2}$
for part b)
the solutions say i am wrong.
I did this:
$c$ $\sum\limits_{n=0}^{\infty} a^n = \frac{c}{1a} = 1$
therefore
$c = 1a^2$ (from part a)
The answer is not this. Solutions are:
$\sum\limits_{x=1}^{\infty} c(a^2)^x = 1$
$ ...$
$c = \frac{a^{2x}(1a^2)}{a^2}$
Why do we begin from $x=1$ and not $x=0$ when summing this series? Is this always the case for these questions? How do I solve part b?
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