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Math Help - How do I prove this is decreasing?

  1. #1
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    How do I prove this is decreasing?

    <br />
\frac{1}{\sqrt{k(k + 1)}}<br />

    This is part of an alternating series and I need to prove that it converges conditionally. The only condition I am stuck on is proving that it's decreasing.
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by TYTY View Post
    <br />
\frac{1}{\sqrt{k(k + 1)}}<br />

    This is part of an alternating series and I need to prove that it converges conditionally. The only condition I am stuck on is proving that it's decreasing.
    f(x) = (x^2 + x)^{-.5}   f'(x)= -.5 (x^2 + x)^{-1.5} (2x + 1)      x > 0
    so clearly the first derivative is negative, hence decreasing.
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  3. #3
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    Quote Originally Posted by apcalculus View Post
    f(x) = (x^2 + x)^{-.5}   f'(x)= -.5 (x^2 + x) (2x + 1)      x > 0
    so clearly the first derivative is negative, hence decreasing.
    Chain rule ftw
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