prove that 1/(2^(2n)) converges

• Mar 25th 2009, 07:05 PM
Mandi_Moo
prove 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, 07:06 PM
wytiaz
comparison test with 1 / 2^n
• Mar 26th 2009, 02:21 PM
Moo
Hello,

Just use basic rules of exponents :
$(a^b)^c=a^{bc}$

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

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

Hint : think geometric