Rewriting Sigma Notation and Sequences

[johnny101]

I'm totally lost on this problem..any help is appreciated. I have to rewritethe sum replacing the index i by k, where i=k +1.
[FONT=&quot]
N(upperlimit)

[sigma notation] [/FONT]i^2* r^n-1 (to right of sigma notation)
[FONT=&quot]
i=1(lower limit) [/FONT]

 

[JeffM]

I'm totally lost on this problem..any help is appreciated. I have to rewritethe sum replacing the index i by k, where i=k +1.

N(upperlimit)

[sigma notation] i^2* r^n-1 (to right of sigma notation)

i=1(lower limit)

Let's make sure that we have the problem stated correctly

\(\displaystyle \displaystyle \left(\sum_{i=1}^ni^2r^n - 1\right).\) Is that it?

\(\displaystyle \displaystyle \left(\sum_{i=1}^ni^2r^{(n - 1)}\right).\) Or is this it?

 

[johnny101]

No parenthesis on the n-i

 

[JeffM]

No parenthesis on the n-i

That really does not answer my question. Furthermore, the 1 seems suddenly to have become an i.

So which is it:

\(\displaystyle A:\ \displaystyle \left(\sum_{i=1}^ni^2r^n\right) - 1.\)

\(\displaystyle B:\ \displaystyle \left(\sum_{i=1}^ni^2r^n - 1\right).\)

\(\displaystyle C:\ \displaystyle \left(\sum_{i=1}^ni^2r^{n - 1}\right).\)

\(\displaystyle D:\ \displaystyle \left(\sum_{i=1}^ni^2r^n - i\right).\)

\(\displaystyle E:\ \displaystyle \left(\sum_{i=1}^ni^2r^{n - i}\right).\)

 

[HallsofIvy]

I'm totally lost on this problem..any help is appreciated. I have to rewritethe sum replacing the index i by k, where i=k +1.

N(upperlimit)

[sigma notation] i^2* r^n-1 (to right of sigma notation)

i=1(lower limit)

Assuming you mean \(\displaystyle r^{n-1}\) rather than \(\displaystyle r^n- \), you can factor that out: \(\displaystyle r^{n-1}\sum_{i=1}^n i^2\). There is a standard formula for \(\displaystyle \sum_{i= 1}^n i^2\). If you do not know what that is, you could look at a few values: if n= 1 that is just 1. If n= 2 it is 1+ 4= 5. If n= 3, it is 1+ 4+ 9= 14, if n= 4, it is 1+ 4+ 9+ 16= 30, if n= 5, it is 1+ 4+ 9+ 16+ 25= 55, etc. It might help to realize "a sum of mth powers is a m+1 degree polynomial.