http://www.nytimes.com/2011/12/30/world/asia/china-unveils-ambitious-plan-to-explore-space.html?_r=1&hpw
http://en.wikipedia.org/wiki/Chinese_space_program
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The Professor, The Pretender and The Physicist.1
P-series
A generalization of the harmonic series is the p-series, defined as:
\sum_{n=1}^{\infty}\frac{1}{n^p},\!
for any positive real number p. When p = 1, the p-series is the harmonic series, which diverges. Either the integral test or the Cauchy condensation test shows that the p-series converges for all p > 1 (in which case it is called the over-harmonic series) and diverges for all p ≤ 1. If p > 1 then the sum of the p-series is ΞΆ(p), i.e., the Riemann zeta function evaluated at p.
link->Harmonic Series
p-Series Convergence
The p-series is given by
sum (1..inf) 1/np = 1/1p + 1/2p + 1/3p + ...
where p > 0 by definition.
If p > 1, then the series converges.
If 0 < p <= 1 then the series diverges.
A generalization of the harmonic series is the p-series, defined as:
\sum_{n=1}^{\infty}\frac{1}{n^p},\!
for any positive real number p. When p = 1, the p-series is the harmonic series, which diverges. Either the integral test or the Cauchy condensation test shows that the p-series converges for all p > 1 (in which case it is called the over-harmonic series) and diverges for all p ≤ 1. If p > 1 then the sum of the p-series is ΞΆ(p), i.e., the Riemann zeta function evaluated at p.
link->Harmonic Series
p-Series Convergence
The p-series is given by
sum (1..inf) 1/np = 1/1p + 1/2p + 1/3p + ...
where p > 0 by definition.
If p > 1, then the series converges.
If 0 < p <= 1 then the series diverges.
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