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Home » College Playground » Calculus - Real Analysis » Unsolved and Proposed Problems
 
A beautiful series
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harazi
Birch & Swinnerton Dyer
Birch & Swinnerton Dyer

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#1
A beautiful series
Study the convergence of sum(n>=1) (-1)^[sqrt(n)]/n, where [] is the integer part.
Source: AMM (I don't know the year or issue).

PostPosted: Fri Jan 09, 2004 4:50 am  Back to top 
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Moubinool
Navier-Stokes Equations
Navier-Stokes Equations

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#2
More beautiful
You also have

\sum (-1)^[sqrt(n)]/n^a

If a>1 the serie converge

If a \leq 0 the serie is divergent

If 0 < a \leq 1/2 the serie is also divergent

If 1/2 < a \leq 1 the serie is convergent

PostPosted: Fri Jan 09, 2004 9:44 am  Back to top 
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