The population of a local species of beetle can be found using an infinite geometric series where a1 = 960 and the common ratio is one forth. Write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.

the summation of 960 times one fourth to the i minus 1 power, from i equals 1 to infinity. ; the sum is 1,280

the summation of 960 times one fourth to the i minus 1 power, from i equals 1 to infinity. ; the sum is divergent

the summation of 960 times one fourth to the i power, from i equals 1 to infinity. ; the sum is 1,280

Question

The population of a local species of beetle can be found using an infinite geometric series where a1 = 960 and the common ratio is one forth. Write the sum in sigma notation, and calculate the sum (if possible) that will be the upper limit of this population.

 the summation of 960 times one fourth to the i minus 1 power, from i equals 1 to infinity. ; the sum is 1,280

 the summation of 960 times one fourth to the i minus 1 power, from i equals 1 to infinity. ; the sum is divergent

 the summation of 960 times one fourth to the i power, from i equals 1 to infinity. ; the sum is 1,280

anonymous · Answer

the summation of 960 times one fourth to the i power, from i equals 1 to infinity. ; the series is divergent

anonymous · Answer

@ganeshie8

anonymous · Answer

I need help on this @ganeshie8

anonymous · Answer

Please @ganeshie8

anonymous · Answer

At least can I tell what I would respond @ganeshie8

ganeshie8 · Answer

$$\large \sum \limits_{i=1}^{\infty}  960 \left(\frac{1}{4}\right)^{i-1}$$

ganeshie8 · Answer

familiar with infinite geometric series formula ?

anonymous · Answer

Yes @ganeshie8

ganeshie8 · Answer

use it and find the infinite sum

ganeshie8 · Answer

$$\large S_{\infty} = \dfrac{a_1}{1-r}$$

ganeshie8 · Answer

$a_1$ = 960
$r$ = 1/4

plugin and simplify

anonymous · Answer

1280

ganeshie8 · Answer

yes!

anonymous · Answer

Ok so the answer would be A or C

ganeshie8 · Answer

A