Tagged Questions
3
votes
2answers
94 views
Is there an algebraic solution to $e^{-x/a}+e^{-x/b}=1$ ($a\neq b$, $a,b$ constants)?
Is there an algebraic solution for the to find the intersection of the following two functions for values of $x\geq 0$:
$$f_1(x)=1-2e^{-x/a}=f_2(x)=-1+2e^{-x/b}$$
$a$ and $b$ are positive constants.
...
2
votes
1answer
301 views
Closed form for $\sum_{k=0}^{n} \cos( t \sqrt{k} )$?
I would like to know if there a closed form solution for the sum:
$$ S_n(t) = \sum_{k=0}^{n} \cos( t \sqrt{k} ) $$
There is obviously an easy answer when the sum is replaced by an integral so this ...
