Question

Evaluate the geometric series. Round to the nearest hundredth. Please help

Answer 1

5.33

Explanation:

The n th term of a geometric series is

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio

4
`((1)/(4)) ^(n-1)` ← is the n th term of a geometric series

with a = 4 and r =
`(1)/(4)`

The sum to n terms of a geometric series is

`S_(n)` =
`(a(1-r^(n)) )/(1-r)`, thus

`S_(10)` =
`(4(1-(1)/(4) ^(10)) )/(1-(1)/(4) )`

=
`(4(1-(1)/(1048576)) )/((3)/(4) )`

=
`(16)/(3)` (
`(1048575)/(1048576)` )

=
`(16)/(3)` × 0.9999....

= 5.33 ( to the nearest hundredth )

Answer 2

5.33.

Explanation:

A1 = 4 and r = 1/4.

The sum of n terms of a G. S, is:

Sn = a1 * (1 - r^n) / (1 - r)

So substituting, we have:

S10 = 4 * [1 - (1/4) ^10] /( 1 - 1/4)

= 5.33