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Mathematical induction

  1. Jan 26, 2014 #1
    1. The problem statement, all variables and given/known data
    (5^2) + (11^2) + (17^2) +...+ (18n-1)^2

    a)Write the sum in sigma notation
    b)Using the sigma identities solve the sum (easy to do)


    2. Relevant equations

    ∑i = .5*k*(k+1) etc

    3. The attempt at a solution

    The problem i'm having is with the 25 and 121. I thought it was

    ∑ (6n-1)^2

    where n goes from 1 to k,
    but I noticed that this does not work for part b then.
    I haven't done induction in 4 years, so unfortunately I forget.

    Unless it isn't from 1 to k, but from 1 to 3k
     
  2. jcsd
  3. Jan 26, 2014 #2

    SammyS

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    How about each term is of the form (6k - 1)^2 ...

    Then k has k go from 1 to ___ . (Fill in the blank.)
     
  4. Jan 26, 2014 #3

    haruspex

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    Yes
    It doesn't? I don't see your difficulty. Please post your working up to where you're stuck.
     
  5. Jan 27, 2014 #4
    yeah it does go from 1 to 3k, not 1 to k because it needs to be for part b equal to

    3n(108n^2 +36n +1)

    Where i was stuck was knowing the bounds
     
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