what is the ratio of this sequence...

1+1/2+1/3+1/4+1/5.....

Question

what is the ratio of this sequence...

1+1/2+1/3+1/4+1/5.....

megannicole51 · Answer

@Hero do u know how do find the ratio?

hero · Answer

Are you looking for the COMMON ratio?

megannicole51 · Answer

the question just says give the first term, which is 1, and the ratio between successive terms

hero · Answer

Okay, so the common ratio is what they want

megannicole51 · Answer

i believe so:)

megannicole51 · Answer

and this is a geometric sequence correct?

hero · Answer

It appears that way. Hang on...

megannicole51 · Answer

okay:)

hero · Answer

Well, I'm pretty sure the common ratio is $\dfrac{1}{n + 1}$

megannicole51 · Answer

yeah i have that written down but isnt there more than i need?

hero · Answer

But I don't think that is geometric

megannicole51 · Answer

what makes a sequence geometric?

hero · Answer

If it was geometric, then you could multiply by the common ratio to produce the next term.

anonymous · Answer

dont you think its a HP

anonymous · Answer

?

hero · Answer

In this case, we have the common ratio but we can't multiply it by the previous term to produce the next term.

hero · Answer

So this is neither arithmetic or geometric.

megannicole51 · Answer

we cant just assume the next terms is (1/6) and that makes it a geometric sequence?

hero · Answer

You can assume what the next terms will be, but you cannot conclude that the sequence is geometric.

hero · Answer

The only thing you can do is try to come up with some kind of recurrence equation.

megannicole51 · Answer

oooh okay....so like with 1-x+x^2-x^3+x^4....would this be geometric?

hero · Answer

Now we're skipping to something else completely different?

megannicole51 · Answer

*wouldn't

megannicole51 · Answer

well we already established that the other question isnt geometric and we already have the ratio...im just trying to understand/distinguish when a sequence is a geometric sequence and these are just some practice problems in my book.

hero · Answer

Not every sequence will be geometric or arithmetic.

hero · Answer

Here's a geometric sequence:

1, 2, 4, 8, 16, 32...

hero · Answer

It has a common ratio of 2

hero · Answer

It is geometric because you can $\color\red{\text{multiply}}$ the previous term by 2 to get the next term.

hero · Answer

The key word is multiply

megannicole51 · Answer

okay that makes sense...so then how would you find the common ratio when you have a + - + - in the sequence...ive been seeing a lot of problems like that in my book but there aren't any examples that show how to solve it or determine if it is a geometric sequence

hero · Answer

You'd have to post one of them first

hartnn · Answer

1-x+x^2-x^3+x^4...

megannicole51 · Answer

that would work lol

megannicole51 · Answer

do u want me to post it on a different thing?

hartnn · Answer

dive next term by current term, 
-x/1 = ... 
x^2/-x =...
-x^3/x^2 =....
are all the answers same ?
if yes, than its geometric with common ratio as the answer to those.
if not, its not geometric

hartnn · Answer

and bdw, there is NO common ratio for initial sequence, 1,1/2,1/3,1/4 ...
its an harmonic sequence.

megannicole51 · Answer

-x right? and it is geometric 

and thank you:)

hartnn · Answer

correct. :)

megannicole51 · Answer

yay!

hero · Answer

@hartnn nice way of showing it without giving the answer.

megannicole51 · Answer

you both did a great job thank you so much:)

hero · Answer

yeah, if it were me, I would have just said -x because the way I approach these I look for a direct relationship between consecutive terms, but @hartnn demonstrated how to properly find a geometric relationship. If you divide the current term by the previous term, then you should be able to find a common ratio if the sequence is geometric.

megannicole51 · Answer

yeah thats a good way to figure it out....and i can do that with every problem right?

hartnn · Answer

every problem of geometric sequence, yes.
for arithmetic sequence, you would have to check the difference between the terms,
next term - current term = constant = common difference d

megannicole51 · Answer

oooh okay

hartnn · Answer

for harmonic sequence, take the reciprocal of each term and see whether they are in arithmetic progression, like your initial problem,
reciprocals are,1,2,3,4,5....
common difference = 2-1 = 3-2 = 4-3 = .... - 1

hartnn · Answer

** = 1

megannicole51 · Answer

omgsh these kinds of problems have so many steps and formulas and tricks to remember!

anonymous · Answer

theres no proper formula to get the sum of a HP.. you just have to solve it..

hartnn · Answer

there are things to understand too, have a look at these for details and other formulas : http://openstudy.com/users/hartnn#/updates/503bb2a0e4b007f9003103b0

megannicole51 · Answer

awesome thank you!!!

hartnn · Answer

you're welcome ^_^

megannicole51 · Answer

if i post another question can you help? it has to do with sums of series

hartnn · Answer

i will surely try :)