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Math Help - Stuck and Frustrated!!!!

  1. #1
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    Stuck and Frustrated!!!!

    Conjecture a formula for the sum 5 + 9 + 13 + ... + (4n + 1)
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  2. #2
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    Hello, bearej50!

    If you know some summation formulas, it's easy.

    . . \sum ^n_{k=1} 1 \:=\:n\qquad\qquad\sum^n_{k=1}k \:=\:\frac{n(n+1)}{2}



    Conjecture a formula for the sum: . 5 + 9 + 13 + \hdots + (4n + 1)

    We have: . \sum^n_{k=1}(4k+1) \;=\;4\sum^n_{k=1}k + \sum^n_{k+1}1 \;=\;4\left(\frac{n(n+1)}{2}\right) + n \;=\;2n^2+3n

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