Question

Use summation notation to write the series 2 + 4 + 6 + 8 + ... for 10 terms.

Answer 1

What's the general term look like

Answer 2

any ideas?

Answer 3

I'm not sure. This question is all I have to go on, and I'm not sure where to begin.

Answer 4

first term: 2

second term: 4

third term: 6

you're adding 2 each time

and you're starting with 2

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so if you start with 2, and you add 2 say n times, then you're left with

2+2n

this only works if you start with n = 0, if you want to start with n = 1, you would have to subtract 2 to get 2+2n-2 = 2n+0 = 2n

So the general term is 2n

Answer 5

where n starts at n = 1

Answer 6

So you can write this in summation notation

Answer 7

Ah, I see. Thanks very much!

Answer 8

this basically says to add up a bunch of 2n terms, but you replace the first n with 1, the second n with 2, etc etc