Use induction to prove that if r is an integer greater than

Solution

solution:

Given 2r > (r + 1)2 and r is an integer greater than 5,

lets say r = 6 then function becomes by substituting r= 6 as,

=> 2(6) > (6 + 1)2

=> 12 > 7*2

=> 12 > 14 is false

lets say r = 7, then,

=> 2(7) > (7 + 1)2

=> 14 > 16 which is also false.

so from mathematical induction as it is false for initial values we cant proceed for further k and k+1 values where k is any integer.

so by mathematical induction given inequality is false.