series sigma notation? (1 Viewer)

[kloudsurfer]

Hey,

I was away when we did this topic and my textbook doesnt explain it at all!

Could someone please explain the whole idea to me? Im so confused!!!

Here are a few questions from my book. What do all the numbers mean? How do you do such questions?



1)
5
Σ 3r^2
r=1



2)
7
Σ 5n-6
3

Any help would be much appreciated!
Thanks in advance!

 

[watatank]

5
Σ 3r^2
r=1

its what you call a summation, relatively simple concept.

in the first one you start your summation with the bottom thing, in this case r = 1, then add for each succesive integer, replacing r = 2, then add the thing for when r = 3, etc, till you reach the thing at the top, which in this case is 5.

first one would be...

3(1)² + 3(2)² + 3(3)² + 3(4)² + 3(5)²

3(1) + 3(4) + 3(9) + 3(16) + 3(25) = 3(55) = 165

very garbled explanation I know, hopefully the working out helps you out more. :wave:

 

[PC]

It's also good to learn how the sigma notation relates to APs and GPs, otherwise why else is it in the topic.

The second question is actually an AP.series sigma notation?

7
Σ 5n-6 = [5(3)-6] + [5(4)-6] + [5(5)-6] + [5(6)-6] + [5(7)-6]
3
= 9 + 14 + 19 + 24 + 29
= 95

This is really an AP where Tn = 5n – 6 and you need to do S₇ – S₂.

How would you work out this sum?

1000
Σ 3k + 4
k = 10

You can't do this one term by term!

 

[z600]

The formula to the right of your sigma sign is the rule that the sequence follows. The term below your sigma sign is the first term of "n" in the formula. To find the first term simply sub that number into n. The number above your signma sign is the last term of n.

 

[kloudsurfer]

Oooh ok I get it now.

Thanks everyone!

 

[bos1234]

It's also good to learn how the sigma notation relates to APs and GPs, otherwise why else is it in the topic.

The second question is actually an AP.series sigma notation?

7
Σ 5n-6 = [5(3)-6] + [5(4)-6] + [5(5)-6] + [5(6)-6] + [5(7)-6]
3
= 9 + 14 + 19 + 24 + 29
= 95

This is really an AP where Tn = 5n – 6 and you need to do S₇ – S₂.

How would you work out this sum?

1000
Σ 3k + 4
k = 10

You can't do this one term by term!

How you do this?

Tn = Sn - Sn-1
Sn = Tn + Sn-1
Sn = 3004 + Sn-1

Sn-1=(T1+T2 + T3 + .. + Tn-1)

=34+37+40+...+3001
=989(3001+34)

Sn = 3004 + 989(3001+34)

Is it like this or something wrong?