suitebrunokach
suitebrunokach suitebrunokach
  • 03-04-2017
  • Mathematics
contestada

Convergence of the series sin(na)/ln(10)^n

Respuesta :

LammettHash
LammettHash LammettHash
  • 03-04-2017
Recall that [tex]|\sin x|\le1[/tex], so this is an alternating series.

The series will then converge iff [tex]\left|\dfrac{\sin na}{\ln10^n}\right|\to0[/tex] as [tex]n\to\infty[/tex] and this summand is non-increasing.

You have

[tex]\left|\dfrac{\sin na}{\ln10^n}\right|\le\dfrac1{\ln10^n}=\dfrac1{n\ln10}\to0[/tex]

and [tex]\dfrac1{n\ln10}[/tex] is clearly strictly decreasing. This means the alternating series converges.
Answer Link

Otras preguntas

What Does "Turning of the Tide" Mean?
Which of the following is the equation of a line parallel to the line y=3x+2, passing through the point (10,1)? A. 3x - y=29 B. 3x + y=29 C. -3x - y=29 D. 3x +
A microscope is set so it makes an object appear 4 x 10`2 times larger than its actual size. A virus has a diameter of of 2 x 10`-7 meter. how large will the di
How do I factor 2y^2 - y - 10
what is an undefined nuclear region containing only nucleic acid
Is There Still Slavery in the World? Please help me :)
what are at least 5 general PowerPoint guidelines that's you find useful and provide an example of how you would use each in real life setting
Ryker is given the graph of the function y= 1/2x^2 - 4 . He wants to find the zeros of the function but is unable to read them exactly from the graph. Find the
Sam and lou need a total of 1 foot of wire for a science project.sam wire is 8 out of 2 n lou is 7 out of 8.Do they have enough.
what is a prefix for marine