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# Arithmetic series in sigma notation

Sal writes the arithmetic sum 7+9+11+...+403+405 in sigma notation. There are actually two common ways of doing this.

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• How about (k=1) on bottom, 200 on top, and (5+2k) to the right of the sigma?
• That is another way of getting the same arithmetic series. Clever thinking!
• express the series in sigma notation
2+3+4+9+8+27+16+81
• I am not an expert and I could have the wrong answer anyway.
I am going to give you a hint: notice the numbers they seem familiar, did you figure it out ?
they are the powers of 2,3 added together !

so they can be written like this:
4
Σ ( 2^x + 3^x )
x=1
(1 vote)
• At , what did Sal say 2 - 1 is 2...? I got confused by that. Was it an error or it actually has something to do with the calculation? Or he probably meant that when K=2 in 2(k-1)....2 minus 1 is 1, times 2 which equals to 2...?
• Two questions: What does n mean? Doesn't it symbolize the term number? And:
If I have the infinite arithmetic series 8+12+16+20+..., how would my sigma notation look like? For this example, would 8 be n=1, 12 be n=2, 16 be n=3,...?
I have that n=1 and goes to infinity with the expression 8+4(n-1).
But my textbook has a different answer. It says n=2 and goes into infinity with the expression 4n. But why n=2? That means that my second term (it being 12) somehow equals to 8.
I really hope someone will understand what I mean..Pls help!
(1 vote)
• How would you get the answer to a problem where you already have the sum with the terms after it...
8
Σ -2+5n
n=2

How would you solve that? I am just completely confused...what am I solving for?
(1 vote)
• You're trying to find the value of the equation. It wants you to find out what the terms from the second term to the eighth term add up to.

1.Plug in the numbers from 2 to 8 for n (so plug in 2, 3, 4....all the way to 8.

2. add the numbers together (so if you plugged 2 in, you would get 8, and then if you plugged in 3, you would get 13, and so on until 8, and then you would add those numbers together)

3. now you've found the value! (it's 161)

This got me confused, too. Thank you, actually, for asking this; it made me learn the lesson better because I wanted to help you out. Hope this helps!
(1 vote)
• I am still easily mixed when it's the right situation to add the 1st value. For instance, in this video, when k=1, in the 2nd expression, the 1st value will still be "7", which is already counted in the sum, why the n becomes 200 instead 199?
(1 vote)
• or how about sum(2k+1), k=3 to 202
(1 vote)