Solving Math Sequence Homework with Help and Pointers

[Mike_Winegar]

Homework Statement

[PLAIN]http://webwork2.math.utah.edu/webwork2_files/tmp/equations/a4/32b370a8c66b49443277f94aa0edf51.png

Homework Equations

The equations that I can see in my book and online look nothing like this problem.

The Attempt at a Solution

Really just looking for a pointer in the right direction...What to look up in my book/online.

I'm assuming it's looking for a summation seeing as the symbol is included, it's just that the problem doesn't look like any others in my book.

 

[tiny-tim]

Hi Mike!

(have a sigma: ∑ )

Isn't it just 1/1 + 1/2 + 1/3 ?

 

[Mike_Winegar]

That is what it was looking for. So for problems that look like that, I add one to K for each term? Then add that to the previous term?

 

[gb7nash]

Before this problem, have you been introduced to the summation sign, start index and end index yet?

In any case, I'll give you a similar example:

\sum_{k=1}^4 k = 1 + 2 + 3 + 4 = 10

Basically, the k is just a placeholder in the summand. The k=1 means that the first value you plug in for k is 1, then you plug in 2, ... all the way until 4. Then you add them all up.

Another harder example is:

\sum_{k=1}^5 \frac{1}{1+k}

Do you think you could solve this one? Once you're able to solve this, your problem will be trivial.

Hi Mike!

(have a sigma: ∑ )

Isn't it just 1/1 + 1/2 + 1/3 ?

You gave him the answer!

 

[tiny-tim]

You gave him the answer!

nooo …

mike still has to add it! ​

 

[Mike_Winegar]

Before this problem, have you been introduced to the summation sign, start index and end index yet?

In any case, I'll give you a similar example:

\sum_{k=1}^4 k = 1 + 2 + 3 + 4 = 10

Basically, the k is just a placeholder in the summand. The k=1 means that the first value you plug in for k is 1, then you plug in 2, ... all the way until 4. Then you add them all up.

Another harder example is:

\sum_{k=1}^5 \frac{1}{1+k}

Do you think you could solve this one? Once you're able to solve this, your problem will be trivial.



You gave him the answer!

So on the one you were referring to, the fully written out terms would be

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

Right? If so, I think I've got it.

 

[gb7nash]

So on the one you were referring to, the fully written out terms would be

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

Right? If so, I think I've got it.

Parentheses are very important. I'm assuming you mean:

\frac{1}{2} + \frac{1}{1+2} + \frac{1}{1+3} + \frac{1}{1+4} + \frac{1}{1+5}

?

 

[Mike_Winegar]

Parentheses are very important. I'm assuming you mean:

\frac{1}{2} + \frac{1}{1+2} + \frac{1}{1+3} + \frac{1}{1+4} + \frac{1}{1+5}

?

Haha, exactly...I'll keep that in mind. Thanks for your help!

 

[gb7nash]

no problem