Linked Questions
11 questions linked to/from Closed form formula for $\sum\limits_{k=1}^n k^k$
3
votes
1
answer
1k
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Sum of self power [duplicate]
Is there a formula to calculate the sum of a number to the power of this same number, like:
$$1^1 + 2^2 + 3^3 + 4^4 + 5^5 + ... + n^n$$?
or
$$x^x + (x+1)^{(x+1)} + (x+2)^{(x+2)} + ... + (x+n)^{(x+...
- 2,041
10
votes
2
answers
703
views
Is there any general formula for $S = 1^1 + 2^2 + 3^3 + \dotsb+(n - 1)^{n - 1} + n^n, n \in N$? [duplicate]
Is there any general formula to sum following series:
$$S = 1^1 + 2^2 + 3^3 + \dotsb+(n - 1)^{n - 1} + n^n, n \in N$$
I mean for $S = f(n)$, is there a formula to compute $f(n)$?
- 321
1
vote
1
answer
192
views
Formula to calculate sum of $k^k $ upto $n$ terms. [duplicate]
What will be the general formula for the series: $1^1 + 2^2 + 3^3 + 4^4\ldots$
The series diverges, but can we have a formula to find the sum of $n$ terms.
- 412
3
votes
0
answers
119
views
How to find $\sum_{k=1}^n k^k$? [duplicate]
Actually question which I found:
Find the sum of the series $1^1+2^2+3^3+ \cdots +n^n $
This question has been bothering me since a long time. Any help would be appreciated!
- 1,664
4
votes
0
answers
71
views
Is there a formula to calculate the following sum? [duplicate]
I tried googling, but I may not be searching with correct terms.
$$\sum_{k=1}^{n} k^k = 1^1 + 2^2 +3^3 + 4^4 + \cdots + n^n$$
So, is there a formula to calculate this?
- 181
1
vote
0
answers
89
views
How to find out the sum of the series $1^1+2^2 +\ldots+n^n?$ [duplicate]
Recently, I was exploring different ways to find out the sum of series but I've one in my mind to which I didn't have a sol. to. It goes :$$\sum_{i=1}^n i^i$$
Does anyone have a solution to this ?
user1104020
2
votes
0
answers
67
views
Closed form for $\sum_{n=1}^{m} n^n$ [duplicate]
I would like to ask if anyone would help me to find a general formula for the sum of m members of the following series.
\begin{equation}
\sum_{n=1}^{m} n^n = 1^1+2^2+\cdots + m^m
\end{equation}
...
user675788
1
vote
0
answers
41
views
A partial sum formula [duplicate]
I'm very familiar with partial sums and such little bit hard once, but I was wondering is there a partial sum formula for that
$$\displaystyle\sum_{n=1}^k n^n$$
I have tried with Wolfram alpha but I ...
- 21
4
votes
3
answers
171
views
$\lim_{n\to\infty}{\left({\sum_{k=1}^nk^k}\right)/{n^n}}=1$?
I'm interested in the following sum $S_n$.
$$S_n:=\sum_{k=1}^nk^k=1^1+2^2+3^3+\cdots+n^n.$$
Letting $T_n:={S_n}/{n^n}$, wolfram tells us the followings.
$$T_5=1.09216, T_{10}\approx1.04051, T_{30}\...
- 145k
1
vote
1
answer
123
views
Does it exist a recursive formula that approximates $\sum_{k=1}^n k^k\,$?
Does it exist a recursive formula that approximates $\sum_{k=1}^n k^k\,$?
Defined $\,S_n=\sum_{k=1}^n k^k$, I am looking for a relation $\,S_{n+1}\sim f(n)\cdot S_n\,$, with $\,S_1=1$ and $f(n)\,$ a ...
- 1,828
2
votes
0
answers
142
views
Why there isn't any formula to calculate $\sum\limits_{k=1}^n{k^k}$ explicitly?
I've looked over this Closed form formula for $\sum\limits_{k=1}^n k^k$ but it doesn't have any explicit formula, only the bounds.
So, is it the case that no general formula can exist to calculate ...
- 2,411