(b) Prove that 2m ≤ m! + 2 for m ¤ N. (c) For any nonzero real number x, prove ---3 i=1 = 1- x -n

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A: Now, since we assumed 3k>k, we can substitute k with 3k in the inequality: 3k+1>3k Since ,…

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Q: n² + n+ 8 2 He has just shown you a convincing proof that if the equation is true for any integer k…

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Q: d) Prove that −1 < x < 0 implies that |x³ − 2x + 1| < 1.26|x − 1].

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Q: For a natural number n, we define n! = 1-2-3 (n − 1). n. - For example: 2! = 1-2, 3! = 1-2-3 = 6,…

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Q: (c) Prove that for n ≥ 1, n [27/7/2≤2- j² 1 n

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Q: Prove an+1 = (an2+ 1) / 2 with a1 = 2 is monotonic increasing.

A: Solution:-

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Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

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Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

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Q: the real number line which equals 1 Qs-, n=1 " + ] ကျေ 18+

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Q: Provide either a proof or a counterexample for  For all positive real numbers x, x^2 - x ≥ 0

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