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Math Help - interval of convergence of a power series

  1. #1
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    interval of convergence of a power series

    need help figuring out what R is for the following power series...


    summation from 0 to infinity {[(1+5^n)/n!]x^n]}
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  2. #2
    Super Member PaulRS's Avatar
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    Remember that: e^x=1+x+\frac{1}{2!}\cdot{x^2}+\frac{1}{3!}\cdot{x  ^3}+... for all real x

    You can even calculate your sum considering the identity above .
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  3. #3
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    i didnt get how u changed the whole numerator of the summation to sin(k).. it was 1+5^n, n! ... where did 1+5^n go?
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  4. #4
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    Quote Originally Posted by PaulRS View Post
    Remember that: e^x=1+x+\frac{1}{2!}\cdot{x^2}+\frac{1}{3!}\cdot{x  ^3}+... for all real x
    What do you think that as to do with it posted series?
    I dare say nothing!

    Quote Originally Posted by ramzouzy View Post
    need help figuring out what R is for the following power series...
    summation from 0 to infinity {[(1+5^n)/n!]x^n]}
    Have you used either the ratio or the root test?
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  5. #5
    Super Member PaulRS's Avatar
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    Angry

    I suggested:

    e^x+e^{5\cdot{x}}=\sum_{n=0}^{\infty}{\left(\frac{  1+5^n}{n!}\right)}\cdot{x^n} for all real x which is the series you wanted


    I do not see sin (n) there


    But if you want to do it by the root test you just have to remember that \lim_{n\rightarrow{+\infty}}\frac{\sqrt[n]{n!}}{\frac{n}{e}}=1
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