We often say that log (1+x) = x - x^2/2 + x^3/3 etc. Is the statement true for x = 500 (or may be larger values?) If not, why?

Can anyone give a definite answer to this?

Question

We often say that  log (1+x) =  x - x^2/2 + x^3/3 etc. Is the statement true for x = 500 (or may be larger values?) If not, why?

Can anyone give a definite answer to this?

ganeshie8 · Answer

@eliassaab

anonymous · Answer

The above series converges for |x|<1
So the answer is no for x=500

anonymous · Answer

$$
\ln (1+500.)\approx6.21661\

\frac{x^3}{3}-\frac{x^2}{2}+x=4.15422\times 10^7 \text{ fpr } x=500
$$

anonymous · Answer

So,due to convergence it is not possible.
But, can u say for what values the series is possible.

tkhunny · Answer

Series Convergence is NOT a finite process.  Any time you cut it off at some finite point, there is no equality.

0) Equality - Not Finite

However, with appropriate error estimates, you may be able to (in decreasing order of precision):

1) Get close enough so that the error cannot be measured by any existing device.
2) Get close enough to build a useful device.
3) Get close enough to verify homework results.