Mathematics
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OpenStudy (anonymous):
urgent HELP!
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OpenStudy (anonymous):
evaluate each finite series for the specifiednumber of terms
80-40+20-...,n=8
jimthompson5910 (jim_thompson5910):
use the formula
S = a*(1-r^n)/(1-r)
where in this case
a = 80
r = -0.5
n = 8
OpenStudy (anonymous):
oh ok! can u help with two more
OpenStudy (anonymous):
determine whether each infinite geometric series converges or diverges. if converges stat the sum
150+30+6+...
-10-20-40-...
jimthompson5910 (jim_thompson5910):
can you identify the value of r for each?
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OpenStudy (anonymous):
first one is 5
OpenStudy (anonymous):
other one is .5
OpenStudy (anonymous):
is that correct @jim_thompson5910
jimthompson5910 (jim_thompson5910):
150 ---> 30 means you divide by 5
or that you multiply by 1/5 = 0.2
jimthompson5910 (jim_thompson5910):
so the first r value is r = 0.2
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jimthompson5910 (jim_thompson5910):
since |r| <1, we know it converges
OpenStudy (anonymous):
oh .. what about the other one
jimthompson5910 (jim_thompson5910):
to find the infinite sum, use this formula
S = a/(1-r)
jimthompson5910 (jim_thompson5910):
in the first one, a = 150, r = 0.2
OpenStudy (anonymous):
Yeah i got that! what about the second one
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jimthompson5910 (jim_thompson5910):
-10-20-40-...
a = -10
r = 2 (since -20 divided by -10 = 2)
because r > 1, this series diverges
jimthompson5910 (jim_thompson5910):
actually because |r| > 1, this series diverges
OpenStudy (anonymous):
oh...i think i undersand! thanks so much! have a good night!
jimthompson5910 (jim_thompson5910):
you're welcome