Sum of Sequence: Find the Solution | Homework Help

[nicnicman]

Homework Statement

Find the sum of the sequence:
2, -2/3, 2/9, -2/27, 2/81, . . .

Homework Equations

The Attempt at a Solution

I can see that the number is multiplied by -1/3, but I'm unsure of how to find the sum.

Any pointers?

 

[hedipaldi]

use the formula for the sum of geometric sequence.

 

[Mark44]

Homework Statement

Find the sum of the sequence:
2, -2/3, 2/9, -2/27, 2/81, . . .

Homework Equations

The Attempt at a Solution

I can see that the number is multiplied by -1/3, but I'm unsure of how to find the sum.

Any pointers?

This is a geometric sequence. There's a formula for finding the sum of a geometric series.

 

[FeynmanIsCool]

aⁿ⁺¹-1/a-1

 

[FeynmanIsCool]

Summed over n: [itex]\sum[/itex]a^k=aⁿ⁺¹-1/a-1

 

[Mark44]

aⁿ⁺¹-1/a-1

Use parentheses!

What you wrote is a_{n + 1} - (1/a) - 1

Summed over n: [itex]\sum[/itex]a^k=aⁿ⁺¹-1/a-1

 

[FeynmanIsCool]

haha good note, your right. I have bad habits when it comes to those things

 

[nicnicman]

Thanks for the help!

I came up with 1 41/81 using the formula. This also equals the sum of the numbers in the sequence (in my original post).

So, I guess it's correct.

 

[nicnicman]

Although, this is in infinite geometric set so should I be using this formula:

S∞ = a1/(1-r), where a1 = the first term in the sequence, and r is the ratio.

 

[nicnicman]

So the answer would be 1 1/2. Correct?

 

[Dick]

So the answer would be 1 1/2. Correct?

Yes, it's 3/2.

 

[nicnicman]

Thanks for the reassurance.