Question

Help with geometric sequences and series please!! Need to know how to solve this problem!

Answer 1

whats the problem

Answer 2

sorry it wasnt posting before!

Answer 3

I am really lost on how to solve it. do you know how to do questions like this?

Answer 4

@hartnn are you able to help with this?

Answer 5

@Abhisar any help?

Answer 6

@dan815 sorry for just tagging random people but i cant figure it out!

Answer 7

ok

Answer 8

u can factor out the 4

Answer 9

sum 4* 2^i=4*sum 2^i
sum 2^i = 2+4+8....+2^9+2^10
2*sum 2^i-sum2^i = 2^11-2
sum2^i(2-1)=2^11-2
sum2^i=2^11-2
4*sum2^i=4*(2^11-2)

Answer 10

im not sure thats what we are learning hahaha that looks very different

Answer 11

i can go step by step

Answer 12

if u want to learn

Answer 13

we usually put it into a formula like the sum of infinite series

Answer 14

or sum of finite series

Answer 15

like these.

Answer 16

let S be that expression they gave u
S=4*2^1+4*2^2+4*2^3....+4*2^10

Answer 17

does this make sense so far

Answer 18

oops i attached the wrong picture. but yes somewhat

Answer 19

i am rewriting the summation notation in terms

Answer 20

and since 4=2^2

Answer 21

we can rewrite it as
S=4*2^1+4*2^2+4*2^3....+4*2^10
=2^3+2^4+2^5......+2^12

Answer 22

make sense so far?

Answer 23

yes i think im following

Answer 24

sorry my computer has issues with openstudy! got booted off for a second.

Answer 25

here is the picture i was trying to attach before.

Answer 26

okay now we can do a trick here

Answer 27

S=2^3+2^4+2^5......+2^12
2*S=2^4+2^5+2^6....+2^13

2*S-S=2^13-2^3
S(2-1)=2^13-2^3
S=2^13-2^3

Answer 28

okay i believe i get what you are saying. but that cant be my answer can it?

Answer 29

S=a^1+a^2+a^3......+a^k
a*S=a^2+a^3+a^4....+2^(k+1)

a*S-S=a^(k+1)-a
S(a-1)=a^(k+1)-a
S=(a^(k+1)-a)/(a-1)

Answer 30

that is the formula u put up there

Answer 31

it comes from the same method

Answer 32

in our case 2 is the geometric factor if the factor is changed to r then u get that same formula

Answer 33

just see if u can figure this out, u can forget the geometric series formula if u understand this http://prntscr.com/5pno2t

Answer 34

is it D?

Answer 35

@cwrw238 any ideas?

Answer 36

@SolomonZelman