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
$\frac{a_1}{1-r}$
a1=-4
r=1/3

$\frac{-4}{1-1/3}$=$\frac{-4}{2/3}$=-12/2=-6
it has a sum of -6




sum of gemoetric sequence is
$\frac{a_1(1-r^n)}{1-r}$
a1=6
r=2
n=10
$\frac{6(1-2^{10})}{1-2}$
$\frac{6(1-2^{10})}{-1}$
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