Question

In a question of power series representation at
http://tutorial.math.lamar.edu/Classes/CalcII/PowerSeriesandFunctions.aspx
in example 5, how do we assume/find the value of x is 0

Answer 1

We are not assuming that x is 0. You could choose another integer to evaluate the constant. The author of the example stated that he chose 0 because it makes it easy to evaluate. If you want to, choose another integer and find the constant using your choice of integer.

Answer 2

that's the reason he chose 0 but where this 0 has come from?

Answer 3

We can find the constant of integration, C, by plugging in a value of x. A good choice is since that will make the series easy to evaluate.

Answer 4

What value of x would you like to choose?

Answer 5

x can be any number that does not result in a negative argument.

Answer 6

so in such situation we will always have to plugin 0 ?

Answer 7

You may plug in the integer of your choice. How old are you? Perhaps you would like to use that integer as a replacement for x. Try to choose something that is easy to evaluate.

Answer 8

You do not HAVE to choose 0. The author chose 0 because it made the problem easy.

Answer 9

I would rather like to stick on the question instead of answering what my age is

Answer 10

I'm afraid you didn't get my point.

Answer 11

sorry what's that?

Answer 12

ohhh sorry got it

Answer 13

so in situation it's always good to pick zero in order to make the evaluation easy

Answer 14

but if we will chose something else then the answer will be different? isn't?

Answer 15

Yes. Pick 0 to make the evaluation easy.

Answer 16

as if we chose 1 then the answer is different from the answer which has been deduced by taking 0

Answer 17

I don't know what you would get is x were 1. You would then have to choose a value for n if you wanted to find C

Answer 18

I solved it it's true for any value

Answer 19

if we solve it for x = 1 then C = ln4 + ln4/5

Answer 20

which gives the same value as C = ln 5

Answer 21

thanks anyway

Answer 22

Excellent.