Convergence of a Cauchy sequence

SANGHERA.JAS
Messages
50
Reaction score
0
Since I don't know how to use latex I have posed my question in word file.
Yours help is greatly appreciated.
 

Attachments

Physics news on Phys.org
If the author has already shown that the statement is equivalent to the statement including the absolute value of q (alone in the absolute value, nothing else with it) then to show it for q<0 would give the same result, as the absolute value would make q positive.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Showing Uniform Convergence of Cauchy Sequence of Functions
Replies
6
Views
3K
Does each norm on vector space become discontinuous when restricted to S^1?
Replies
1
Views
1K
Proof that two equivalent sequences are both Cauchy sequences
Replies
8
Views
3K
Understanding the Use of Min in Cauchy Sequences
Replies
1
Views
1K
Proving convergence of sequence from convergent subsequences
Replies
15
Views
2K
Doubt regarding the series ##\sum [\sqrt{n+1} - \sqrt{n}\,]##
Replies
17
Views
2K
Prove that the sequence does not have a convergent subsequence
Replies
4
Views
1K
Bounded and monotonic sequences - Convergence
Replies
7
Views
2K
Finding limit of the Fibonacci sequence
Replies
8
Views
2K
Bounded non-decreasing sequence is convergent
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top