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Math Help - Series induction (real analysis)

  1. #1
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    Series induction (real analysis)

    2 questions

    #1) prove by induction that 1/k! is less than or equal to 1/(2k-1))

    I showed the base case and assumed it to be true for all k and want to show that it is true for k+1 or that 1/(k+1)! <= 1/2k

    From my assumption I can either multiply both sides by 1/2 and get that 1/2*k! <= 1/(2k) which gets me the correct rhs or I can multiply both sides by 1/(k+1) to get the correct lhs side but can't get both at once, any suggestions?

    #2) Let sn = the sum from k=1 to n of 1/k! and tn = the sum from k=1 to n of 1/(2k-1)
    Prove by induction that sn<=tn


    No idea how to do this after showing my base and assuming true for n any help would be great

    Thanks a lot!
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  2. #2
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    Re: Series induction (real analysis)

    Series induction (real analysis)-mi.png
    Thanks from Johngalt13
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