Unformatted text preview: 1  1 1 1 1 N 1 1 1 fl v'2 v'2 ( . en n ,L. ...i=1 Vi v'1 + v'2 + v'2' ow + 72 + 2 >""2 +""2 smce .J2 ~ 1.4) and 4 + l' = 24 = .J2. Thus, 2::~=1 ~ > .Jii when n = 2. Now suppose that k ~ 2 and the given assertion is true for n = k; that is, suppose 2:::=1 ~ > .jk. We have to prove that the assertion is true for n = k + 1; that is, we have to prove that 2:::':;:; ~ > v'k"+1, Now k+l 1 L:i=1 Vi k 1 1 L:+== i=1 Vi v'k"+1 1 > .jk + ~ (by the induction hypothesis) yk+1 .jkv'k"+1 + 1 v'k"+1 Vk2+k+1 > v'k2+1 = k+1 =Jk+1 v'k"+1 v'k"+1 Jk + 1 as desired. By the Principle of Mathematical Induction, the given assertion is true for all n ~ 2. (i) [BBJ With n = 2, 2(2)  1 = 3 ~ 2(2)  2 =2, so the inequality holds. Now assume k ~ 2 and...
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 Summer '10
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 Graph Theory, Mathematical Induction, Natural number, Mathematical logic, Mathematical proof

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