Extract a variable from the following summation

Question

Is it possible to extract the variable a from the following summation and hence write the summation as a times 'something', or similar?

$$n/a = \sum_{i=1}^n 1/(a+x_i)$$

Is there an lhs ? Do the $x_i$ show a pattern ? – Claude Leibovici Apr 14 '17 at 10:09 — Claude Leibovici, Apr 14 '17 at 10:09

score 1 · Accepted Answer · answered Apr 14 '17 at 09:28

1

Let $g(a,x_1,\dots,x_n)=\sum_{i=1}^n \frac{1}{(a+x_i)}$

If you could write $g(a,x_1,\dots,x_n) = a f(x_1,\dots,x_n)$ for some function $f$ then the second partial derivative of $g$ with respect to $a$ would be zero. However, it isn't zero so you can't do that so there can be no way to factor out the $a$.

answered Apr 14 '17 at 09:28

Bernard W

2,141

ok, thanks, will leave as is in my solution – tony1kenobi Apr 14 '17 at 10:09

Extract a variable from the following summation

1 Answers1