Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

Using cauchy's criterion |a_n+p - a_n|

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SIGN UP FOR FREE
Using \[|a_{n+p}-a _{n}|<\] Show that \[a_{n}=\frac{ \cos x }{ 3 }+\frac{ \cos 2x }{ 3^{2} } + \frac{ \cos 3x }{ 3^{3} } + .... +\frac{ \cos nx }{ 3^{n} }\] is a cauchy sequence
\[|a_{n+p}-a _{n}|< \epsilon \]
since cosine is bounded above by 1 and below by -1 i believe this is the same as saying \[\frac{1}{3^{n+p}}-\frac{1}{3^n}|<\epsilon\]

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

will that be enough ?:D
should be although maybe we need to be a little careful
the largest the absolute value can be is if one cosine is -1 and the other is 1 but the difference is bounded by 2
so you can factor a 2 out of the whole thing, makes no difference in the proof
by which i mean \[|\frac{\cos((n+p)x)}{a^{n+p}}-\frac{\cos(nx)}{a^n}\leq 2|\frac{1}{3^{n+p}}-\frac{1}{3^n}|\]
\(a\) should be \(3\)
|dw:1353710521064:dw|
Thank you both very much :D

Not the answer you are looking for?

Search for more explanations.

Ask your own question