-------- My attempts: a) We need to show that if P(n) is true then P(n-1) also is. , so and . Not sure what to do now. b) Need to show . No idea what to do next.
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Originally Posted by scorpion007 -------- My attempts: a) We need to show that if P(n) is true then P(n-1) also is. , so and . Not sure what to do now. Take , so that b) Need to show . No idea what to do next. Since P(n) is true we get: (1) (2) Now multiply both inequalities above and use P(2) for the right side!: . Well, now just re-arrange cosmetically a little the rightmost side and you have there P(2n) Tonio
Thanks!
I noticed you multiplied both sides of the inequality by different amounts. Is it true in general that ?
Hello scorpion007! Originally Posted by scorpion007 I noticed you multiplied both sides of the inequality by different amounts. Is it true in general that ? If a, b, c and d are integers then take and . In this case means which is true and means which is also true. Now, means and therefore which is false. Best wishes, Seppel
Thanks Seppel! Ah, but what if , like in the original question? Perhaps then it is true?
Originally Posted by scorpion007 Thanks Seppel! Ah, but what if , like in the original question? Perhaps then it is true? Yes, it is then true.
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