By recognizing the series
((3/4))+((3/4)^2)/2+((3/4)^3)/3+.....+…
as a Taylor series evaluated at a particular value of x, find the sum of the convergent series.
sum = ??
Originally I was thinking this looked like the ln(x) expansion but it doesn't go from + to - so I'm not sure what to use. e^x expansion also looks like it could be a possibility but its divided by n! not just n+1...
Help please?
((3/4))+((3/4)^2)/2+((3/4)^3)/3+.....+…
as a Taylor series evaluated at a particular value of x, find the sum of the convergent series.
sum = ??
Originally I was thinking this looked like the ln(x) expansion but it doesn't go from + to - so I'm not sure what to use. e^x expansion also looks like it could be a possibility but its divided by n! not just n+1...
Help please?
-
I think this series is the expression for -ln(1-x) = x+x^2/2+x^3/3+x^4/4
-ln(1-3/4) = -ln(0.25) = -(-1.386)
If all else fails, go with this!
-ln(1-3/4) = -ln(0.25) = -(-1.386)
If all else fails, go with this!