Question

Is 1/2 a standard when trying to determine an error approximation?

Answer 1

for example:

how many terms of the series: 1- 1/2 + 1/3 - 1/4 + ... are needed to compute the sum correct to two decimal places?

Answer 2

the answer shows:

\[a_n=1/n\text{ so choose "n" such that...}\]
\[\frac{1}{n+1}<\frac{1}{2}x10^{-2}\]
why the 1/2?

Answer 3

Are you going up to infiniti
\[\sum _{n=1}^{\infty } (-1)^{n+1}\left(\frac{1}{n}\right)\]

Answer 4

?

Answer 5

yes

Answer 6

Okay, it converges to ln(2)

Answer 7

right, the sum of the series is ln(2)

but is there any reason why they used ".005" in their error approximation to 2 decimal points? Why not use .001 or .007 or someelse?

Answer 8

I know there are better reason, but if there are none it might be because it is in middle