1. The problem statement, all variables and given/known data If [tex]\sum^{n}_{r=0} \frac{1}{^{n}C_{r}} = a[/tex], then find the value of [tex]\sum^{n}_{r=0} \frac{r}{^{n}C_{r}}[/tex] in terms of a and n.[/tex] 3. The attempt at a solution I tried to write down the terms of both the series, but to no avail. i cant think of anything.Please shed some light.
Hi ritwik06! Hint: suppose n = 12. Then [tex]\sum^{n}_{r=0} \frac{1}{^{n}C_{r}}[/tex] = (0!12! + 1!11! + 2!10! + 3!9! + …)/12! So what is [tex]\sum^{n}_{r=0} \frac{r}{^{n}C_{r}}[/tex] ?
Hi tim, I'm not seeing how this helps to solve the problem. You have a term dependent r in each summand, so how do we express it in a?
Thank god! Somebody helped me. But Tim, I wonder what you wish to convey... Please could you be more explicit
Consider: [tex] \sum^{n}_{r=0} \frac{n-r}{^{n}C_{r}} [/tex] How does that compare with: [tex] \sum^{n}_{r=0} \frac{r}{^{n}C_{r}} [/tex] Does that give you any ideas??
Hi ritwik06!! Have you got this now … you haven't said? If you haven't, then follow Dick's hint … it's much better than mine! (same for the other thread)
That's nice of you to say, tiny-tim. Thanks. :) Now you've got me curious. ritwik06, did you get it? It's surprising easy if you think about it right, and pretty nonobvious if you don't. It took me a while.