anonymous
  • anonymous
Determine a function which is represented by that summation given below
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\sum _{n=1}^{\infty } \text{nx}^n\]
anonymous
  • anonymous
what this?
amistre64
  • amistre64
x + 2x^2 + 3x^3 + 4x^4 + ... + nx^(n)+.... like that?

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anonymous
  • anonymous
no,you know how f(x)=e^x is represented by \[1+x+x^2/2!+..... \] so this is reverse where you are trying to figure out function based on series given
amistre64
  • amistre64
or do we want this to be a backwards taylor series?
amistre64
  • amistre64
y = ? y' = 1 y''=2 y'''=3 y'''' = 4 then right?
amistre64
  • amistre64
or do we account for the factorials also i spose
anonymous
  • anonymous
This can be written as a geometric series. Use that to find the function that represents the summation.
anonymous
  • anonymous
you got it, backward taylor series
anonymous
  • anonymous
You don't need to do that amister.
amistre64
  • amistre64
lol.... i do if I wanna understand whats going on ;)
anonymous
  • anonymous
Haha. ok.
anonymous
  • anonymous
what factorial
amistre64
  • amistre64
taylor has factorials under them; i just assume they are a part of it
anonymous
  • anonymous
no, it is the series, I think we want the function that it represent
amistre64
  • amistre64
1 1 2 6 120 720 5040 40320 362880 3628800 those things
amistre64
  • amistre64
i got more reading to do about series to be able to understand them better :)
anonymous
  • anonymous
So Taylor polynomial of a function is this. We want the function?
anonymous
  • anonymous
Trial & error might help
anonymous
  • anonymous
\[\sum_{n=1}^{Infinity}nx^n\] = x+2x^2+3x^3+.....+nx^n

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