PLease help i've totally forgotten how to do this i know it has something to do with the sequences of partial sums.

Show that (the sum from n=1-infinity) of 1/(2^(2n)) converges.

Sorry bout the crap way of writing it.

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- Mar 25th 2009, 06:05 PMMandi_Mooprove that 1/(2^(2n)) converges
PLease help i've totally forgotten how to do this i know it has something to do with the sequences of partial sums.

Show that (the sum from n=1-infinity) of 1/(2^(2n)) converges.

Sorry bout the crap way of writing it. - Mar 25th 2009, 06:06 PMwytiaz
comparison test with 1 / 2^n

- Mar 26th 2009, 01:21 PMMoo
Hello,

Just use basic rules of exponents :

$\displaystyle (a^b)^c=a^{bc}$

Hence $\displaystyle 2^{2n}=(2^2)^n=4^n$

Is $\displaystyle \sum_{n=1}^\infty \frac{1}{4^n}$ a convergent series ?

Hint : think geometric