SOLUTION: Find the range of values of x for which the infinite series 1 + lnx/2 +(lnx)^2/(2^2) + (lnx)^3/(2^3) + (lnx)^4/(2^4)+... converges. Find the sum to infinity when x=e^(1/2).

Question 1069243: Find the range of values of x for which the infinite series 1 +
lnx/2 +(lnx)^2/(2^2) + (lnx)^3/(2^3) + (lnx)^4/(2^4)+... converges. Find the sum to infinity when x=e^(1/2).
Answer by trsomas23@gmail.com(17) (Show Source): You can put this solution on YOUR website!
It is an infinite geometric series with common ratio
r =
The series converges if
|r| < 1
< 1
ln(x) < 2
x <
Sum of series =
=
When x = , then the sum of the series
=
=
=
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