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Math Help - Power series

  1. #1
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    Power series

    a_nx^n, b_nx^n are two power series with radius of convergence R1, R2, respectively.
    If R1 is different than R2, how can i prove that the radius of convergence of the power series (a_n + b_n)x^n is min{R1, R2}?
    And what can be said about the radius of cenvergence if R1=R2?

    Thanks for any help
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  2. #2
    MHF Contributor matheagle's Avatar
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    since the center is 0 for both 'series'
    I would like to see a sum here
    the sum of the two series is convergent for all x between \left(-\min\{R1,R2\},\min\{R1,R2\}\right)
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