Determine the convergence or divergence of the series.sum_{n=3}^inftyfrac{1}{n(ln n)[ln(ln n)]^4}

Ayaana Buck

Ayaana Buck

Answered question


Determine the convergence or divergence of the series.

Answer & Explanation



Skilled2021-01-11Added 106 answers

A series, n=mf(n) converges if the value of the integral, mf(n) is finite and diverges if it is infinite.
For the series, n=31n(lnn)[ln(lnn)]4, the integral is 31x(lnx)[ln(lnx)]4dx
Let ln(lnx)=y,1xlnxdx=dy
At x=3,y=ln(ln3)
at x=,y=
So, the integral becomes:
Since, the value of the integral is finite. Thus, the sum of the series converges.

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