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anonymous
 one year ago
Power Series Question Picture on inside
anonymous
 one year ago
Power Series Question Picture on inside

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 1 }{ 14x }= \sum_{0}^{\infty} (4x)^n \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I then differentiated both sides

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 4 }{ (14x)^2 }= \sum_{n=1}^{\infty} n(4x)^{n1} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 8 }{ (14x)^2 }= 2 \sum_{n=1}^{\infty} n(4x)^{n1}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but this isn't giving me the proper coefficients did i make a mistake somewhere?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1what is your derivative of 8(14x)^(2) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Did i need to take the derivative of that?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1\[f(x)=0!c_0+\sum_{1}c_nx^n\] \[f'(x)=1!c_1+\sum_{2}c_nx^n\] \[f''(x)=2!c_2+\sum_{3}c_nx^n\] \[f'''(x)=3!c_3+\sum_{4}c_nx^n\] etc ....

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1at x=0, or whatever you center it as, the summation part goes to 0, and we are left with a solution for the coeffs

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1\[c_n=\frac{f^{(n)}(a)}{n!}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh.. I thought that was only for Taylor series. I'll try it out thank you.

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1taylor series are power series ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1sometimes a power series can be generated by simply working the division ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.1spose we integrate your function up to 2/(14x) 2+2^3x+2^5x^3  14x  2 (22^3x) 8x (8x2^5x^2) 32x^2 (32x^22^7x^3) F(x) = sum 2^(2n+1) x^n take the derivative f(x) = sum n 2^(2n+1) x^(n1)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you for all your help I understand where I went wrong now and I got the answer.
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