Question

0

Answer 1

Are you sure about that common ratio?

Answer 2

yep

Answer 3

Okay, so the ratio is greater than 1, which means the series diverges and there is no upper limit to the summation.

Answer 4

so if it is divergent there is no infinite sum?

Answer 5

Correct, a divergent series either increases without bound (approaches \(\infty\)) or oscillates between \(-\infty\) and \(\infty\).

Answer 6

ok can u help with one more? @SithsAndGiggles

Answer 7

sure

Answer 8

The population of a type of local bass can be found using an infinite geometric series where a1 = 72 and the common ratio is \[\frac{ 1 }{ 4 }\]. Find the sum of this infinite series that will be the upper limit of this population.

Answer 9

Alright, this is a convergent series so everything should work nicely. (Convergent because the common ratio is between -1 and 1.)
\[\sum_{n=1}^\infty ar^{n-1}\]
is the form of the series, and we're given that the first term \(a_1\) is 72. This means
\[a_1=\sum_{n=1}^1 ar^{n-1}=ar^{1-1}=72~~\Rightarrow~~a=72\]
and so the series is
\[\sum_{n=1}^\infty 72\left(\frac{1}{4}\right)^{n-1}\]
The sum of this kind of series is given by
\[\frac{a}{1-r}\]

Answer 10

is it 96?

Answer 11

Yes

Answer 12

thanks!! :)

Answer 13

yw