the (-1)^(r-1) determines the sign before the term.its to determine the sign (if it is positive or negative). Look at the last term for the blue graph (-x^4/4). In this case r=4 and the sign is negative. If we do (-1)^4 we get +1 making the sign positive which would be incorrect. If we put the power as r-1 then when we put in r=4 the power becomes 3. (-1)^3 is -1 which means the sign will be negative which is correct. generating the general solution is very hard as you have to look and identify small details then figure how to express them in the general solution term.
excuse me guys could you help me out, i am trying to make a code for the ln function using taylor polynomials without calling predefined functions. I seem to have trouble in calculating for ln(0.1) because it needs a lot of terms (or iterations in coding) to be accurate to 10^-6 or 6 decimal places. I would like to ask if there can be some special ln rule that can help me lessen the number of terms in the taylor series to calculate for ln (0.1)?
its to determine the sign (if it is positive or negative). Look at the last term for the blue graph (-x^4/4). In this case r=4 and the sign is negative. If we do (-1)^4 we get +1 making the sign positive which would be incorrect. If we put the power as r-1 then when we put in r=4 the power becomes 3. (-1)^3 is -1 which means the sign will be negative which is correct.
Great video, thank you!
I don't understand how to generate the general solution term with r in it
the (-1)^(r-1) determines the sign before the term.its to determine the sign (if it is positive or negative). Look at the last term for the blue graph (-x^4/4). In this case r=4 and the sign is negative. If we do (-1)^4 we get +1 making the sign positive which would be incorrect. If we put the power as r-1 then when we put in r=4 the power becomes 3. (-1)^3 is -1 which means the sign will be negative which is correct. generating the general solution is very hard as you have to look and identify small details then figure how to express them in the general solution term.
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What do you use for writing (software and hardware)?
excuse me guys could you help me out, i am trying to make a code for the ln function using taylor polynomials without calling predefined functions. I seem to have trouble in calculating for ln(0.1) because it needs a lot of terms (or iterations in coding) to be accurate to 10^-6 or 6 decimal places. I would like to ask if there can be some special ln rule that can help me lessen the number of terms in the taylor series to calculate for ln (0.1)?
If I were to sum the first n terms of log(1+x), what would it be? Help?
Why does the last term of the series ln (1+ x) is (-1)^r-1 x x^r all over r. Why is it r-1?
its to determine the sign (if it is positive or negative). Look at the last term for the blue graph (-x^4/4). In this case r=4 and the sign is negative. If we do (-1)^4 we get +1 making the sign positive which would be incorrect. If we put the power as r-1 then when we put in r=4 the power becomes 3. (-1)^3 is -1 which means the sign will be negative which is correct.
nai hua tho deakh lena wtf