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Math Help - need help for proof with simple function

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    40

    need help for proof with simple function


    I really don't know what to do for part a. Help with b would be nice, too.


    Thanks.
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  2. #2
    Member arpitagarwal82's Avatar
    Joined
    Feb 2009
    Posts
    103
    a)

    to prove f(0) = 0

    f(x + y) = f(x) + f(y)
    put x = y =0
    we get
    f(0 + 0) = f(0) + f(0)
    => f(0) = 2f(0)
    => f(0) = 0

    b)f(n) = f(1 + (n-1))
    = f(1) + f(n-1)
    = f(1) + f(1 + (n-2))
    = f(1) + f(1) + f(n-2)
    and so on

    = f(1) + f(1) + f(1) + f(1) + f(1) --- ntime
    = nf(n)

    you can also use mathematical induction for proving part b of problem
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