Homework Help: Find the sum of the first n terms

1. Apr 25, 2014

lionely

1. The problem statement, all variables and given/known data

Find the sum of the first n terms of the sequence U1, U2, U3...... Ur

2. Relevant equations

3. The attempt at a solution

$$\sum_{r = 1}^n (1 + (-1)^r) = n + (-1)^n$$

But I don't this is right... any help?

2. Apr 25, 2014

Staff: Mentor

What are U1, U2, etc.?

3. Apr 25, 2014

lionely

It doesn't say this is the exact question, it just wants me to find the Sum of the first n terms of this case

4. Apr 25, 2014

SammyS

Staff Emeritus
Like before, write out the first few terms of the series.

5. Apr 25, 2014

lionely

It alternates between 1 and -1 so would the sum would alternate between -1 and 0... so... 1/2( (-1)^n -1) ?

6. Apr 25, 2014

SammyS

Staff Emeritus
You said, "It" alternates ...

What is the "It" you refer to?

The series never decreases.

Write out the first several terms of the sequence, then the first several terms of the series.

7. Apr 25, 2014

lionely

when I mean "it" I meant the sequence. I'm sorry and what I typed above was in reference to the part I did not understand, the sum of (-1)^n. I understand the sum of 1 to n terms = n.

so my final answer is $$n + 1/2((-1)^n -1)$$

8. Apr 25, 2014

SammyS

Staff Emeritus
That looks pretty good.

S1 = 0

S2 = 2

S3 = 2

S4 = 4

S5 = 4

...