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