Question

Show that r(s-r+1)>s if 1< r

Answer 1

given  s > r > 1.       I suppose this is missed in the question given.

let us take the expression:
 E =    r ( s - r + 1) - s
    =   r s  - r² + r  - s
   =    s (r - 1) - r² + r
   =    s (r - 1) - r (r - 1)
   =   (s - r ) (r - 1)        => this is positive as   s > r  and  r > 1

Hence the expression  E is positive.  proves the given question as E > 0