Question

What is the sum of the geometric series ? I attached an image. Its in sigma notation

Answer 1

I think you need to use "geometric series partial sum formula"

Answer 2

look it up in your notes and see if you can find it..

Answer 3

okay!

Answer 4

An=A1+(n-1) -2

Answer 5

nope

Answer 6

ohh wait thats for arithmetic right?

Answer 7

exactly thats for airthmetic sequence

but we want "geometric series partial sum" formula

Answer 8

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

Answer 9

Yes thats the one

Answer 10

\[S_n = a_1 \dfrac{1-r^n}{1-r}\]

find out the values and plug in

Answer 11

im not sure what i would plug in for r

Answer 12

we can eyeball by comparing with :
\[\sum\limits_{n=0}^M a(r)^n\]

we get \(r = 3/4\)

Answer 13

and you get first term by plugging in n=0 :

\[3\left(\dfrac{3}{4}\right)^0 = 3(1) = 3\]

so \(a =3 \)

Answer 14

since there are 19 terms, we have \(n=19\)

Answer 15

then the partial sum would be
\[\large 3\dfrac{1- \left(\frac{3}{4}\right)^{19}}{1-\frac{3}{4}}\]

simplify

Answer 16

11.94 ?

Answer 17

Thank you so much this makes so much more sense now !

Answer 18

umm there is an error in the solution, the values of n finish at 18... and not 19 as shown in the formula

Answer 19

thanks but to find n( the numbers in the solution) , you subtract the limits & add one

Answer 20

so n= 19

Answer 21

@campbell_st

Answer 22

Yep! im getting 11.949
which rounds to 11.9\(\color{Red}{5}\)

Answer 23

awesome ! thanks again!

Answer 24

yw!