prove an identity for any integer

rue82
125 ●2 ●4 ●13

Let $n$ be a positive integer and $m = (m_1, \ldots, m_n)$ an $n$ -dimensional vector of real numbers. Let $g$ be a real number.

I want to prove, for any $n$ and $m$ , an equality of the form $\sum_{i=1}^n f_i (m,g) = 0$ where the function $f_i$ is a rational function of $m$ and $g$ .

Of course it's easy to check this by substituting finite values of $n$ , but is there a way in Sage to prove it for any integer?

Comments

Sage supports symbolic computations like in this example:

sage: k, m = var('k, m')
sage: sum(1/k^4, k, 1, oo)
1/90*pi^4
sage: sum(binomial(m,k), k, 0, m)
2^m

Max Alekseyev ( 4 years ago )

Thanks, I did see that, although in my case it just prints the sums and does not simplify them to zero.

rue82 ( 4 years ago )

Then it's possible that your problem is out for reach for Sage and needs to be addressed by analytic rather than computational methods. You may ask for help at https://math.stackexchange.com/

Max Alekseyev ( 4 years ago )

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prove an identity for any integer