Showing posts with label summation. Show all posts
Showing posts with label summation. Show all posts
Monday, October 1, 2018
Sum over hypercube
Let $n$ be a positive integer, and suppose $a = a_1, \dots, a_{2019}$ is a sequence of integers each ranging from $1,\dots,n$.
Determine the sum of
$$\sum_a \frac{a_1 - a_2 + a_3 + \dots -a_{2018} + a_{2019}}{a_1 + \dots + a_{2019}}$$
Where the sum is taken over all possible sequences in that range.
Labels:
Algebra,
expected value,
probability,
summation,
symmetric
Monday, November 16, 2009
Simplifying Series
Let $a_n = \binom{2n}{n}$ and $b_n = \binom{3n}{n}$. Find a more compact expression for:
$A(x) = a_0 + a_1x + a_2x^2 +\cdots + a_nx^n + \cdots$
$B(x) = b_0 + b_1x + b_2x^2 +\cdots + b_nx^n + \cdots$
$A(x) = a_0 + a_1x + a_2x^2 +\cdots + a_nx^n + \cdots$
$B(x) = b_0 + b_1x + b_2x^2 +\cdots + b_nx^n + \cdots$
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