[Solution] If p is a constant, show that the series 1+∑_n=3^∞ (1)/(n • ln n •[ln (ln n)]^p) converges if p>1, b. diverges if p ≤q

Question: If $p$ is a constant, show that the series

\[1+\sum_{n=3}^{\infty} \frac{1}{n \cdot \ln n \cdot[\ln (\ln n)]^{p}}\]

converges if $p>1$, b. diverges if $p \leq 1 .$ In general, if $f_{1}(x)=x, f_{n+1}(x)=\ln \left(f_{n}(x)\right)$, and $n$ takes on the values $1,2,3, \ldots$, we find that $f_{2}(x)=\ln x, f_{3}(x)=\ln (\ln x)$, and

so on. If $f_{n}(a)>1$, then

\[\int_{a}^{\infty} \frac{d x}{f_{1}(x) f_{2}(x) \cdots f_{n}(x)\left(f_{n+1}(x)\right)^{p}}\]

Price: $2.99

Solution: The downloadable solution consists of 1 pages
Deliverable: Word Document

∴ Other downloads you may be interested in ∴

[Step-by-Step] The convergence of ∑_n=1^∞[(-1)^n-1 x^n]

[Solution Library] Evaluate ∫(dx)/(x(x+1)(x+2)• •

(Step-by-Step) For each x >0, let G(x)=∫_0^∞ e^-xtdt. Prove

[Solution] Use tabular integration to compute ∫e^3x sin

(Solved) Use tabular integration to compute ∫ cos 5x sin

Sample Hypothesis Testing Problems - MathCracker.com

[Solution] If p is a constant, show that the series 1+∑_n=3^∞ (1)/(n • ln n •[ln (ln n)]^p) converges if p>1, b. diverges if p ≤q

reset password

sign up