Find the sum of the first n terms

[lionely]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

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

 

[Mark44]

Homework Statement

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

What are U₁, U₂, etc.?

Homework Equations

The Attempt at a Solution

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

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

 

[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

 

[SammyS]

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

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

 

[lionely]

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

 

[SammyS]

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

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.

 

[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 $$ n + 1/2((-1)^n -1)$$

 

[SammyS]

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 $$ n + 1/2((-1)^n -1)$$

That looks pretty good.

S₁ = 0

S₂ = 2

S₃ = 2

S₄ = 4

S₅ = 4

...