Recent content by bincy

Hii All, Can anyone give me a hint to evaluate $$\sum_{n=1}^{\infty}\frac{a^{n}}{n^{1-m}}$$; Here $$0<m,\,a<1$$. Please note that the summation converges and $$< \frac{a}{1-a}$$. A tighter upper bound can be achieved as $$1+\int_{1}^{\infty}\frac{a^{x}}{x^{1-m}}dx$$. Is there any way to...

Hi all, Can I get an upper bound of the below expression in terms of $\textbf{all } r,v,b$? $\displaystyle \sum_{k=1}^{\infty} \quad \frac{r^{kb}}{\left(1-r^{k+1}\right)^{a}-\left(1-r^{k}\right)^{a}} \quad : b>1 , 0<r,a<1$ Can we atleast obtain an upper bound for $\sum_{k=1}^{\infty}...

Hii, Thanks everyone. Now I understand that, to prove only the lower bound, we don't have to do much. It is just $\sum_{i=1}^{n}i^{k}>\int_{0}^{n}x^{k}dx$ (Dividing the area of the curve into rectangles) regards, Bincy

Hii All, $ \sum_{i=1}^{x}i^{N}:N>2 $. Is there any approximated lower bound for the above summation? Is it > $ \frac{1}{N+1}x^{(N+1)}$ ? If yes, how to prove that?regards, Bincy

Hi, Eg. Say I have 10 balls. My $a_i=\frac{1}{2}$ irrespective of $i$, Then in the first take, i may take 5, second 2, 3rd 2, 4th 1. This is just a sample path. In an average i take 5 in 1st, 2( round it from $\frac{5}{2}$) in the second, 1( $\frac{3}{2}$ )in the third, 1( $\frac{2}{2}$...

Hii Everyone, A a box contains $N$ balls. In each step, we remove some number of balls from the box according to some distribution, where the distributions are independent but not identical. We don't know any other details of the distributions but their averages. It means in...

Can you please explain me the source of these formula?

Hii Everyone, \int\frac{1}{x^{r}-1}dx where r is a real no. greater than 1regards, Bincy

Thanks a ton (Bow)(Bow)

Hello, \underset{n\rightarrow\infty}{Lt} \frac{n^{(1+q)}}{e^{(\frac{1}{2})n^{(1-q)}}} where0<q<1 I tried using L' Hospitals rule but could not able to do since same pattern was repeating. I strongly believe that the limit is 0.regards, Bincy

Hii everyone, I have a sequence {ai,1<= i <=k} where i know the sum of this sequence(say x). I want to know the sum of another sequence {bi, 1<=i <=k}(at least a tight upper bound) where bi=ai*(1/2^i). Or in other words, if you know the sum of the ratio sequence and sum of 1 sequence, how to...

Hii Every one, In one paper I read that, {\displaystyle \sum_{j\geq1}\left(\frac{c*m*logm}{2^{\left(\frac{j-1}{2}\right)}}\right)}^{j}<=m^{o(logm)} with the explanation "Since the sum is of the same order as its largest term". c>0, m>=2. m is an integer. Can anyone pls...

Thanks. May I know the source of it?

Hii, Thanks for your spontaneous reply. But what i want is a function f(x), such that Ln(x)<=f(x) which can mimic the variations of Ln(x). For eg (1-x)/x is a lower bound of Ln[x].

Hii everyone, Can anyone tell me a decent upper bound of Ln[x](which can mimic Ln[x]) where x is in [0,1]regards, Bincy