While pedantic, the above "expression" is NOT = 1/3
1/3 is the limit, as the sum of n=1 to n -> infinity, of (1/4)^n
The "result" converges towards 1/3. You can get as close to 1/3 as you like, but the result will never quite equal 1/3.
Cheers Dion.
1/3 is the limit, as the sum of n=1 to n -> infinity, of (1/4)^n
The "result" converges towards 1/3. You can get as close to 1/3 as you like, but the result will never quite equal 1/3.
Cheers Dion.
(I do find myself compelled to say that the mathematical convention is that an infinite sum is defined to be equal to the limit of the partial sums, if it exists.)
The convention I have seen is to use the symbol of an arrow such as -> to denote the concept of approaching.
However I did state I was being pedantic.
D.
Anyways, assuming that your comment was in earnest, the arrow is typically used for functions (or sequences). E.g.,
1/n -> 0 as n->infinity
1/4 + 1/16 + ... + 1/4^n -> 1/3
1/4 + 1/16 + ... = 1/3
1/4 + 1/16 + ... -> 1/3
It's exactly like saying lim as x -> 1 of 2x -> 2. You don't write it that way. You write it as lim as x -> 1 of 2x = 2.