Sequences and Discrete Math

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johnny101

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Hello! Any help on this would be great! I'm somewhat lost.

I have to rewrite the sum replacing the index i by k, where i=k +1.

N(upperlimit)

[sigma notation] i^2* r^n-i (to right of sigma notation)*note this is i^2 r^n-i, with no parenthesis and n-i is the exponent to r.

i=1(lower limit)
 
johnny101 said:
Hello! Any help on this would be great! I'm somewhat lost.

I have to rewrite the sum replacing the index i by k, where i=k +1.

N(upperlimit)

[sigma notation] i^2* r^n-i (to right of sigma notation)*note this is i^2 r^n-i, with no parenthesis and n-i is the exponent to r.

i=1(lower limit)
Click to expand...

I wish I could sure what that really says.

But this is my guess: \(\displaystyle \displaystyle\sum\limits_{i = 1}^N {{i^2}{r^{N - i}}} = \sum\limits_{k - 0}^{N - 1} {{{\left( {k + 1} \right)}^2}{r^{N - k - 1}}} \)
 
the way you have it written out is correct, but can you show how you did that, did you factor it out??
 
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