Find the sum of the series or state that the sum does not exist. 5 + 7.5 + 11.25 + ... and 16 + 12 + 9 + ...
the 16+12+9 doesn't exist right?
Do you know what kind of sequence you're dealing with here?
geometric right?
you are correct
Notice how 7.5/5 = 1.5 and 11.25/7.5 = 1.5, so this shows us that we're multiplying each term by 1.5 to get the next term
yes i see that
Now do you know the rule for summing terms in an geometric sequence? Specifically the rule of summing an infinite number of terms.
r<1?
Close, it's more like |r| < 1 If that is true, then the infinite sum exists.
so this sum does not exist
So in the case of r = 1.5, |r| < 1 is false since |1.5| < 1 is false
but the other one is 64 right?
So you are correct, the infinite sum doesn't exist for the first sequence.
The first term is 16. So a = 16 What is the value of r in the second sequence?
.75
Good, so the infinite sum is S = a/(1-r) S = 16/(1-0.75) S = 64 So you are correct.
thanks!
you're welcome
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