Question

the mean of 1,2,2^2,2^3.......2^31 lies in between
a. 2^24 to 2^25
b. 2^25 to 2^26
c. 2^26 to 2^27
d. 2^29 to 2^30
e. 2^23 to 2^24

Answer 1

well, we have a geometric sum of 32 data points

Answer 2

\[\frac{\left(\frac{1-r^{31}}{1-r}\right)}{32}\]

Answer 3

how comes this formula??

Answer 4

a mean is the sum of the parts, divided by the number of parts:

2^0 to 2^31 is 32 parts

the sum of the parts is geometric by definition:

let S = r^0 + r^1 + r^2 + ... + r^31
and -rS = - r^1 - r^2 - ... - r^31 - r^32
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(1-r)S = r^0 - .................................... - r^32

so S = (1 - r^32)/(1-r)

i spose i had a slight error due to the last term

Answer 5

r^n, given n terms .... and n=32 in this case :)

Answer 6

at any rate:
\[\frac{1-2^{32}}{2^5(1-2)}=2^{27}-2^{-5}\]

Answer 7

looks like 2^27 - a fraction, so its between ^26 and ^27