Question about Sigma and Sum Notation

[Bucs44]

Here is the problem I'm at currently. I'm not sure that I'm on the right track or not. Also I'm not sure what numbers I should be plugging into the equation. I think it would be 2 through 6 but...?

The sum of elements in the set {ti | i = 3 } #7 on top of sigma notation

tn = 2n - 1, n greater than or equal to 1

Here is my calculation so far:

i1 + i2 + i3 + i4 + i5 + i6 + i7 = (1-1)+(2-1)+(3-1)+(4-1)+(5-1)+(6-1)+(7-1)

Where do I go next?

 

[Tom1992]

just use the formula sigma(i, i from 1 to n) = n(n+1)/2.

In this question, there are only 7 terms, so you can also add up by hand.

 

[Bucs44]

just use the formula sigma(i, i from 1 to n) = n(n+1)/2.

In this question, there are only 7 terms, so you can also add up by hand.

I don't understand that - why would I be adding if ti = 2n - 1?

 

[cristo]

I don't really understand your question. Is it calculate $$\sum_{n=1}^7t_n$$, where t_n=2n-1?

If not, please could you quote the exact question as written. (NB, click on the formula to get the code for the LaTex equation)

 

[Bucs44]

Yes sorry - I'm not able to write it exactly - don't have math software - but how you have shown it is correct

 

[cristo]

Yes sorry - I'm not able to write it exactly - don't have math software -

Note that the software is preloaded into the forum, and so anyone can write in LaTex. See here for a tutorial.

but how you have shown it is correct

If my sum above is correct, then you simply sum over n in the range 1 to 7. So, $$\sum_{n=1}^7(2n-1)= (2*1-1)+(2*2-1)+ \cdots$$ Do you see where I'm going here? Just plug in the remaining values of n, and then simplify the sum (to obtain a number) which will be the answer.

 

[Bucs44]

Note that the software is preloaded into the forum, and so anyone can write in LaTex. See here for a tutorial.



If my sum above is correct, then you simply sum over n in the range 1 to 7. So, $$\sum_{n=1}^7(2n-1)= (2*1-1)+(2*2-1)+ \cdots$$ Do you see where I'm going here? Just plug in the remaining values of n, and then simplify the sum (to obtain a number) which will be the answer.

Okay - so I do that up to 7 and then add them together or subtract?

I'd get 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49

 

[Bucs44]

Correct me if I'm wrong, but in order to obtain the product, I simply multiply those numbers for my total?

 

[cristo]

Okay - so I do that up to 7 and then add them together or subtract?

I'd get 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49

Thats right, you add the terms.

Correct me if I'm wrong, but in order to obtain the product, I simply multiply those numbers for my total?

Is this a different question now? Do you want to find $$\Pi_{n=1}^7(2n-1)$$? If so, yes, you would multiply the terms.