Find the false statement 1) \(\displaystyle{\sum_{{{n}={2}}}^{{\infty}}}{\frac{{{1}}}{{{n}{\left({\ln{{n}}}\right)}{P}}}}\) converges if

Bryson Whitney

Bryson Whitney

Answered question

2022-04-12

Find the false statement
1) n=21n(lnn)P converges if p>1
2) the integral test does not apply to divergent sequence
3) n=11nP converges if p>1 and diverges if p1
4) If an and f(n) satisfy the requirements of the integral test, and if 1f(x)dx converges, then n=1an=1f(x)dx

Answer & Explanation

star04iks7

star04iks7

Beginner2022-04-13Added 14 answers

Consider the statements:
(a) n=21n(lnn)P converges if p>1 by Cauchy condensation test
Hence, (a) option is true.
(b) The integral test does not apply to divergent sequences
The given statement is false.
n=11anbn< that is convergent and if an0 then |an|<
Thus, the second statement is false.

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