R rand_althor Active Member Joined May 16, 2015 Messages 554 Gender Male HSC 2015 Jun 10, 2015 #1 Could someone please help?
P photastic Well-Known Member Joined Feb 11, 2013 Messages 1,848 Gender Male HSC 2014 Jun 11, 2015 #2 For n = 2, LHS = 400 - 25 = 375 RHS = 225 LHS < RHS n = k 20^k - 5^k > 15^k Prove true n = k + 1 20^k+1 - 5^k+1 > 15^k+1 LHS = 20(20^k) - 5(5^k) > 20[15^k + 5^k] - 5(5^k) = (5+15)(15^k) + 15(5^k) = 15(15^k) + 5(15^k) + 15(5^k) > 15^k+1
For n = 2, LHS = 400 - 25 = 375 RHS = 225 LHS < RHS n = k 20^k - 5^k > 15^k Prove true n = k + 1 20^k+1 - 5^k+1 > 15^k+1 LHS = 20(20^k) - 5(5^k) > 20[15^k + 5^k] - 5(5^k) = (5+15)(15^k) + 15(5^k) = 15(15^k) + 5(15^k) + 15(5^k) > 15^k+1
