3
$\begingroup$

What are the advantages of using one over the other? I mean this in the context of sequences and series. For example, should we let the geometric sequence start from $n=0$ or $n=1$ to get $a_n = a_0r^n$ or $a_n = a_1r^{n-1}$, respectively? Another example is the arithmetic sequence, which changes from $a_0 + dn$ to $a_1 + d(n-1)$ based on which number we start with (0 or 1).

$\endgroup$
  • $\begingroup$ The only advantage of the former, as far as I know, is shorter expressions $\endgroup$ – Yuriy S Jul 10 '16 at 14:17
  • 1
    $\begingroup$ In Taylor series $\sum_0^\infty b_n(x-a)^n$ is the natural way to proceed. $\endgroup$ – André Nicolas Jul 10 '16 at 14:19
3
$\begingroup$

Sometimes one convention is simpler and more natural, and sometimes the other. It is probably best to stick with the convention that you are presented with, if that is a normal one, unless there is a good reason to alter it. It is a good idea not to chop and change from one to the other in a similar context (e.g. arithmetic or geometric sequences): otherwise you may end up forgetting which convention was assumed by the formula that you remember.

Edit: See this answer to a related question for specific examples.

$\endgroup$
0
$\begingroup$

Most computer scientists might argue that numbering should start at zero.

$\endgroup$
  • $\begingroup$ A computer scientist told me long ago: “Computers count from zero; people count from one.” $\endgroup$ – amd Jul 10 '16 at 20:44
  • $\begingroup$ In most programming languages designed for mathematics, indexing begins at 1. Matlab, R, Mathematica, and Fortran are all good examples. $\endgroup$ – Underminer Feb 14 '18 at 16:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.