## MathSofiya Group Title Oh I think I get the idea of stripping out a term now. Simply by taking out an $a_1$ changes where the sum starts? Yes? $\sum_{n=1}^\infty a_n=a_1+\sum_{n=2}^{\infty} a_n$ one year ago one year ago

1. MathSofiya Group Title

so when I have $\sum_{n=1}^{\infty}a_nnx^n=a_1+\sum_{n=2}^{\infty}a_nnx^n$ but it's not n=0? Why?

2. MathSofiya Group Title

I'm trying to start at n=0

3. MathSofiya Group Title

$\sum_{n=1}^{\infty}a_nnx^n \rightarrow \sum_{n=0}^{\infty}a_nnx^n$

4. MathSofiya Group Title

I looked at example 1 a. http://tutorial.math.lamar.edu/Classes/CalcII/Series_Basics.aspx but I'm not trying to do an index shift :C

5. Freyes Group Title

Well do you need to start at 0? because if you want n = 0 you can just make it at the bottom n = 0

6. MathSofiya Group Title

why though?

7. MathSofiya Group Title

why is that all I need to do?

8. Freyes Group Title

$\sum_{n =0}^{\infty}$

9. Freyes Group Title

because in your equation it would work for not getting an answer anyway

10. Freyes Group Title

because multiplying by 0 just leaves the term out basically, so you can have it as n=0 but you won't get an actual term out.

11. Freyes Group Title

if you are trying to get a term out there have to be different conditions met in your equation otherwise it won't work that way. But it looks fine for getting a term out if it's not n = 0.

12. MathSofiya Group Title

by that do you mean that $\sum_{n=1}^{\infty}a_nnx^n=a_1+\sum_{n=0}^{\infty}a_nnx^n$ It leaves the $a_1$out?

13. Freyes Group Title

no

14. MathSofiya Group Title

:(

15. Freyes Group Title

it's right the left part

16. Freyes Group Title

but if you made that n = 0

17. Freyes Group Title

on the left and n= 1 on the right

18. Freyes Group Title

it would be $\alpha _{0}*0*x^0$

19. MathSofiya Group Title

OMG! I think something just clicked!

20. Freyes Group Title

Yeah, you see where im going with it

21. MathSofiya Group Title

no wait, just a second

22. Freyes Group Title

You can have it start at 0.. but it doesnt change anything if you start at 1 in this case

23. MathSofiya Group Title

$\sum_{n=0}^{\infty}a_nnx^n=0$

24. Freyes Group Title

it's like putting 0 + $\sum_{n=1}^{\infty} (insert rest here)$

25. Freyes Group Title

for n = 0

26. Freyes Group Title

I guess if you want to start at 0, it has to be fixed at 0 and you can't change that value for it so it's usually left out of summations and n starts at 1. There are situations where you can have n start at 0 but in you equation those conditions for having a different term at n = 0 is not met.

27. MathSofiya Group Title

I'm a very visual learner. Where you said: "on the left and n= 1 on the right" $\sum_{n=1}^{\infty}a_nnx^n=a_1+\sum_{n=0}^{\infty}a_nnx^n$ ^^^Is wrong I know, but would you mind writing what you mean?

28. MathSofiya Group Title

I'm honestly trying hard to get this...I think we're almost there...sorry =/

29. Freyes Group Title

$\sum_{n=0}^{\infty}a _{n}nx ^{n} = 0 + \sum_{n=1}^{\infty}a _{n}nx ^{n}$

30. Freyes Group Title

using the rule that 0 multiplied by anything is 0

31. MathSofiya Group Title

Thank you, finally!

32. Freyes Group Title

Lol it's ok, glad i could help