Hate to fluff it for you, but we got that on our first induction hw sheet. :p
n(n-1)(n+1)(3n+2)/24 + (n+1)(1+2+3...+n) using assumption
= n(n-1)(n+1)(3n+2)/24 + n(n+1)^2/2
= n(n+1)[(n-1)(3n+2) +12(n+1)]/24
= n(n+1)[3n^2 +11n +10]/24
= n(n+1)(n+2)(3n+5)/24, as required.
All you needed to say was there is a double root at point of contact where the curves are tangential.
(edit: of course showing that the eqn happened to be solving the 2 curves simultaneously.
ishq: yes)
lol the restriction took me a while to get out though...
ARRGH... 2 times 2 is 4, not 3 =/
Seems like a typical CSSA paper.
Q8 is easiest, Q1 is hardest, etc.
xy + yz + zx = 5 (using the results they gave you)
then 1/x + 1/y + 1/x = (xy + yz + zx)/xyz = 5/xyz or 5/xy (by substituting xy = z^2 in an earlier form of the expression)
so z = 1, xy = 1, answer is 5.