Question

Find a formula for Sn, (n is greater than or equal to 1)

1,3,7,15,31

so i know that A1=1 and im not sure what r is...i know that the pattern is 2,4,8,16 so its multiplying by 2 but I hate putting together the equation!

Answer 1

@agent0smith

Answer 2

This one is a bit more difficult... there's no common ratio but you did notice the pattern :D

It's not obvious... but it's 2^n - 1

see the pattern:
1,3,7,15,31
2,4,8,16,32 (this is 2^n.. 2^1, 2^2, 2^3 etc)

notice the top row is all 1 less than the numbers from the bottom row, so the formula is 2^n - 1 (whivh you have to find the sum of...)

Answer 3

isnt it +1 not -?

Answer 4

im sorry i was looking at that wrong lol

Answer 5

no prob :)

Answer 6

wait isnt it 2x+1?

Answer 7

oooh thats right i see it now...lol okay im good:) i have faith in ur answer

Answer 8

haha okay :) Not sure how to find the sum of it though...

Answer 9

i just needed to find the formula so its okay

Answer 10

\[\Large \sum_{n =1 }^{\inf }(2^n -1 ) = \text { I have no idea. }\]

Answer 11

But don;t you need the formula for Sn? that's just the formula for any term, the 2^n - 1

Answer 12

yeah that will work lol

Answer 13

Which? The "I have no idea." answer probably isn't acceptable haha :) but i had an AP physics student write "I have no idea" on an extra credit homework problem... then she drew a turtle. I gave her extra credit for the turtle.

Answer 14

It was a good turtle!

Answer 15

awesome! well my TA grades these homework problems and hes kind of a jerk but hes nice to me so idc and hes been giving me 100% on most of my homeworks so it should work...i dont think i can draw a turtle lol

Answer 16

haha okay well don't put i have no idea unless you can draw a good turtle :D

http://www.wolframalpha.com/input/?i=summation+from+n%3D1+to+infinity+of+%282%5En-1%29 might help.

Answer 17

It was awesome. She drew a diagram of the problem, then wrote "I have no idea." then drew a small turtle.

Answer 18

hahahah awesome!

Answer 19

yep she's an awesome student :D