I have a series like   sum = 1 + 1/2 + 1/3 + ... ... ... + 1/n   Suppose I know the value of n. so what is the formula to calculate sum?
23460
How to find the sum of the following series? $$1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \dots + \frac{1}{n}$$ This is a harmonic progression. So, is the following formula correct? $\frac{(number ~of ~terms)^2}{sum~ of~ all ~the~ denominators}$ $\Rightarrow $ if $\frac{1}{A} + \frac{1}{B} +\frac{1}{C}$ are in H.P. Therefore the sum of the series can be written as : $\Rightarrow \frac{(3)^3}{(A+B+C)}$ Is this correct? Please suggest.
54060
sum of series $\displaystyle \frac{n}{1\cdot 2 \cdot 3}+\frac{n-1}{2\cdot 3\cdot 4}+\frac{n-2}{3\cdot 4 \cdot 5}+\cdots \cdots n$ terms  assuming $\displaystyle S_{n} =\frac{n}{1\cdot 2 \cdot 3}+\frac{n-1}{2\cdot 3\cdot 4}+\frac{n-2}{3\cdot 4 \cdot 5}+\cdots +\frac{n-(n-1)}{n\cdot n+1 \cdot n+2}$  $\displaystyle S_{n} = \sum^{n-1}_{r=0}\frac{n-r}{(r+1)\cdot (r+2) \cdot (r+3)}$  wan, t be able to solve after that , could some help me with this
87518
How do I find the sum of this series?   $$\sum_{n=0}^{\infty}{\sin^{3}\left(3^{n}\right) \over 3^{n}}$$   Hints in the right direction would be appreciated.
104205
I'm trying to find the sum of :   $$\sum_{i=1}^n\frac i {2^i}$$  I've tried to run $i$ from $1$ to $∞$ , and found that the sum is $2$ , i.e :   $$\sum_{i=1}^\infty\frac i {2^i} =2$$  since :  $$(1/2 + 1/4 + 1/8 + \cdots) + (1/4 + 1/8 + 1/16 +\cdots) + (1/8 + 1/16 + \cdots) +\cdots = 1+ 1/2 + 1/4 + 1/8 + \cdots = 2 $$  But when I run $i$ to $n$ , it's a little bit different , can anyone please explain ?   Regards
49569
How to find the sum of this series?  $$\sum_{k=0}^{\infty}\cfrac{{2}^{k}}{\binom{2k+1}{k}}$$  It seems very easy. But I still can not work it out, can anyone help?
20763
Trying to find the sum of the following infinite series:  $$ \displaystyle\sum_{n=1}^{\infty}\frac{{(-1)}^{n-1}}{(2n-1)3^{n-1}}$$  Any ideas on how to find this sum?
96023
Is there a formula for the following sum?  $S_n = 1\cdot2 + 2\cdot 3 + 3\cdot 4 + 4\cdot 5 +\ldots  + n\cdot (n+1)$
97715
My Prof wrote that   $\sum_{n=2}^{\infty} n(n-1)x^{(n-2)} = \frac{2}{(1-x)^3}$  when $-1&lt; x&lt;1$  I do not understand where the above formula comes from. Can someone please explain the steps or provide a hint?   Thanks!
44573
Say you have +1 on first iteration, +2 on second, and so on until N, and you want to know the total.  That's easily calculate using (N * (N + 1) ) / 2.  What's that equation or technique called?
68775
Who knows about the summation of this series: $$\sum\limits_{i=1}^{n}i^m $$  where $m$ is constant and $m\in \mathbb{N}$?  thanks
33804
$$\sum_{r=1}^nr(r+1)=\frac{n(n+1)(n+2)}{3}$$  could you help me with how exactly I work this out?
86275
I am struggling a bit with power series at the moment, and I don't quite understand what this question is asking me to do? Am I meant to form a power series from these, or simply evaluate that series? Any explanation/working is appreciated.  Using power series representation, calculate  $$\sum_{n=1}^\infty \frac{n2^n}{3^n}.$$
64621
Can anyone tell me about the sum of the series $$\sum_{n=1}^\infty \frac{1}{(2n)(2n+1)}?$$ This is not a usual telescoping sum in which all the terms cancel out.
25607
I am confused on the following series: $$\sum\limits_{n=1}^{\infty}\frac{1}{n(n+1)} = 1$$ My calculator reveals that the answer found when evaluating this series is 1. However, I am not sure how it arrives at this conclusion. I understand that partial fractions will be used to create the following equation. I just don't understand how to proceed with the problem. $$\sum\limits_{n=1}^{\infty}\left(\frac{1}{n}-\frac{1}{n+1}\right) = 1$$
100751
How do I find the formula for this sum  $S_n = \sum_{i=1}^n i(i-1)$  Wolfram alpha gives me the correct formula which is $ \frac{1}{3} (n-1)n(n+1)$, but I'm interested in how I get to that and how I can approach this kind of problem in general.
113204
How could the series below be computed ? $$\sum_{k=0}^{\infty}\frac{1}{2^{k!}}$$ It's not a series from a book, but a series I thought of many times, and I didn't manage to figure out what I should do here. I'm just curious to know if there are some known ways for approaching such a series. Thanks!
106805
So I just started learning series, and I am having trouble understanding them. I have a series below:  $$\sum_{n=0}^{\infty} \frac{1}{(2n+1)2^n}$$  Can someone explain to me how I should go about this, from start to finish? I couldn't find any online websites that explained how to find sums, so if you have that, it would be greatly appreciated!