Question

Evaluate these 3 series
(screenshots attached)

Answer 1

a.
n=1 is -4*1=-4
1st term is -4
2nd is -4/3
3rd is -4/9
4th is -4/27

b. converge because -1<r<1

c. as long as -1<r<1, then
the sum of the infnite series is

`(a_1)/(1-r)`
a1=-4
r=1/3


`(-4)/(1-1/3)`=
`(-4)/(2/3)`=-12/2=-6
it has a sum of -6




sum of gemoetric sequence is

`(a_1(1-r^n))/(1-r)`
a1=6
r=2
n=10

`(6(1-2^(10)))/(1-2)`

`(6(1-2^(10)))/(-1)`
6138
2nd answer



3*5+4*5+5*5+6*5+7*5+8*5=
5*(3+4+5+6+7+8)=
165
answer is 4th one