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  3. annotate tl edit 19a1 dev1 1 prove by induction that...

Question: annotate tl edit 19a1 dev1 1 prove by induction that...

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Annotate Tl Edit 19-a1 dev1 1. Prove, by induction, that Vn e N, 1+1+ +n2 = n(n+162n + 1). 2. Let r > 0,rメ1. Prove by induction the formula for the sum of the geometric progression with ratio r: rn+1-1 r -1 3. Prove, by contradiction, that if n3+3 is odd, then n is even. 4. (40, page 72) Find a counterexample, if possible, to the following statements, where r and y are integers: (a) Vz 3y ( 1/y) (b) Va 3y (y2 z < 100) 5. (12 page 113) Prove that either 2- 10s500+15 or 2-10500 + 16 is not a perfect square. N.B. a perfect square is a number of the form n2, with n e N 6. Construct a truth table for the following compound propositions: (a) p^-p (b) (pv-q)→ q (c) (p-q(q-P) (d) (pAq) (pVa) Which of these propositions are tautologies? Are there some propositions which are equivalent to others?
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