# MTH401 Differential Equations GDB Solution Fall 2012

Dear students we have studied in differential equations that an analytical function can be represented in terms of the power series and also using power series we can always determine such an analytical function. In the following GDB, you have to find such an analytical function using the given power series. The limit on the summation is from n = 0 to n = infinity. I mean to say that this is infinite series and have finite sum. Very simple technique would be used here to find such an analytical function. I mean to say that do not use the power series technique to find such an analytical function. Just observe the behaviour and type of the given power series; you can easily find out the required function. Secondly, the interval of convergence of the given power series will decide the domain of the function and also the domain of the derivative of the function. Good Luck for all of them.

If
f(x) = Σ x n ; n = 0 to ∞
Then
Determine the function f(x).
Discuss the domain of f(x).
Discuss the domain of the derivative of f(x).

Opening Date of Graded Discussion Board: 6th Feb. 2013 at 12:01am
Closing Date of Graded Discussion Board: 7th Feb. 2013 at 11:59pm

Solution :