Looks good to me.MozAngeles said:Homework Statement
sum ((x-1)^(2n-2))/((2n-1)!) n=1..infinity?
after doing the ratio test, i found that the radius is from negative infinity to infinity (converges for all x).
is this right?
if not can you steer me in the right direction, please.
Summing a series refers to the process of adding up all the terms in a sequence, starting from the first term to the last. The result of summing a series is called the sum or total of the series.
The "radius" in this context refers to the range of values that the series can be summed over. In this case, the radius is infinite, meaning that the series can be summed over an infinite range of values.
The radius is an important factor to consider because it determines the convergence or divergence of the series. If the radius is finite, the series will converge to a specific value. However, if the radius is infinite, the series may diverge and not have a specific sum.
The radius can be determined by using the ratio test, which involves finding the limit of the absolute value of the ratio of consecutive terms in the series. If this limit is less than 1, the series will converge, and if it is greater than 1, the series will diverge. The radius can also be determined by using other convergence tests such as the integral test or the comparison test.
Yes, the radius of convergence can change depending on the series being summed. Some series may converge over a finite radius, while others may converge over an infinite radius. It is important to determine the radius for each series individually to accurately determine its convergence.