Recent content by danielc

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    Proving Riemann Integral: Non-Negative f(x)=0 $\rightarrow \int^{b}_{a}f=0$

    Homework Statement Suppose f(x):[a,b]\rightarrow\Re is bounded, non-negative and f(x)=0. Prove that \int^{b}_{a}f=0. Homework Equations The Attempt at a Solution I am trying to use the idea that lower sums are zero, and show that the upper sums go to zero as the norm of the...
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    Convergence of a Series with Square Roots and Cubic Terms

    thank you very much , I think I got the idea now .
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    Convergence of a Series with Square Roots and Cubic Terms

    If I make numerator to be k+k=2k instead of k+k^1/2 , does that work? but is it okay to ignore the -4k term in the original denominator ?
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    Convergence of a Series with Square Roots and Cubic Terms

    Base on the behavior of k , I think the series will converges , so I would have to compare it with something larger (called it b) , thus , if b converges than the original series converges. However, I am having hard time figuring out what converging b I should choose which won't violate the...
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    Convergence of a Series with Square Roots and Cubic Terms

    Homework Statement Investigate convergence of \sum\frac{k+k^{1/2}}{k^{3}-4k+3} The Attempt at a Solution I am trying to use comparison test to investigate the convergence , but I am having trouble of finding a correct term to be compared to. please help Homework Statement...