TSR Wiki > Study Help > Subjects and Revision > Mathematics > STEP > STEP III 1997 question 1 solution
(i)
Now plug in x=1 to get:
, as required.
(ii)
So
(iii)
Solution by dvs
![\displaystyle = 4 + 9x + \sum_{n=2}^{\infty} \left[\left(\frac{1}{(n-1)!} + \frac{5}{(n-1)!} + \frac{4}{n!}\right) x^n\right]](http://www.thestudentroom.co.uk/latexrender/pictures/f2/f253135b0d50c58d4fa9fc1ffbf10b14.png "\displaystyle = 4 + 9x + \sum_{n=2}^{\infty} \left[\left(\frac{1}{(n-1)!} + \frac{5}{(n-1)!} + \frac{4}{n!}\right) x^n\right]")
![\displaystyle = 4 + 9x + \sum_{n=2}^{\infty} \left[\frac{n(n-1) + 5n + 4}{n!} x^n\right]](http://www.thestudentroom.co.uk/latexrender/pictures/61/61c5111854885ce31399788451c75715.png "\displaystyle = 4 + 9x + \sum_{n=2}^{\infty} \left[\frac{n(n-1) + 5n + 4}{n!} x^n\right]")
