Question

Determine whether the series converges, and if so find its sum

Answer 1

I'm having trouble understanding why my answer isn't like the one in the book! I'm following all the same steps but I'm getting it all wrong :/

Answer 2

whoops I'm sorry guys this is the problem i need help with!! *

Answer 3

What are your steps?

Answer 4

1. finding the ratio
r= [a sub(n+1)] / [a sub n]
2. find the sum
S= (a)/(1-r)

Answer 5

So, do it here.

Answer 6

ok well sequence is 9/16 , -27/64 , 81/256 ...
r = (-27/64) / (9/16)
= -3/4

Answer 7

S = (9/16) / (1 - (-3/4))
= 9/28

Answer 8

the books answer is "4/7"

Answer 9

Why is your first term 9/16?

Answer 10

because when k=1 it is 9/16 ?

Answer 11

When k = 1, you have (-3/4)^(1-1) = (-3/4)^0.

Answer 12

ohh noooo. i see what i did.. i wrote the exponent as k+1 :/

Answer 13

let me see if i can get the right answer now

Answer 14

i was having the same problem with all the other homework questions i keep getting the answers wrong :/

Answer 15

Well, at least you're getting it. You should get the answer now.
Good job nevertheless.

Answer 16

thank you! maybe after this problem would you mind helping me figure out what I'm doing wrong with another similar problem?

Answer 17

Yeah, post it.

Answer 18

thank you :) the next one is...

Answer 19

for my sequence i got 1/12 , 1/20 , 1/30 ...
r = (1/20) / (1/12)
= 3/5
S = (1/12) / (1-(3/5)) = 5/24

Answer 20

my books answer is "1/3"

Answer 21

That method won't really work here.

Answer 22

hm, i thought maybe that was it. How would this problem be solved :S

Answer 23

Do you know how factorials work?

Answer 24

yes!

Answer 25

Won't want to confuse you. Use the telescoping series.

Answer 26

First, decompose by partial fractions.