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Math Help - 3 fun problems on analysis

  1. #1
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    3 fun problems on analysis

    1. Is the series Sigma (-1)^n * (n!)^2/((2n)!) convergent

    2. Determine the radius of convergence of the power series Sigma
    (-1)^n * ((n+3)/(3^n+4^n)) * x^(3n)

    3. Is the series Sigma n!/(n^n)convergent

    Thx guys!
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  2. #2
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    Quote Originally Posted by luoginator View Post
    1. Is the series Sigma (-1)^n * (n!)^2/((2n)!) convergent

    2. Determine the radius of convergence of the power series Sigma
    (-1)^n * ((n+3)/(3^n+4^n)) * x^(3n)

    3. Is the series Sigma n!/(n^n)convergent

    Thx guys!
    alternating series test/ ratio test can solve all of these, what have you tried ?

    Bobak
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  3. #3
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    umm..ive tried ratio test...but it doesn't seem to be workin properly coz the fraction is sooooooo huge lol....any good idea man?
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  4. #4
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    \frac{\frac{(n+1)!(n+1)!}{(2n+2)!}}{\frac{(n)!(n)!  }{(2n)!}} = \frac{(n+1)^2}{(2n+2)(2n+1)}

    can you finish off?

    Bobak
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  5. #5
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    actually..im worried about 2 and 3....i actually used lim test...like lim ak =0 to test its convergency for question 1....but ur way is nice anyway
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