DP Mathematics HL Questionbank

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Directly related questions

• 18M.2.hl.TZ2.6: Use mathematical induction to prove that \({\left( {1 - a} \right)^n} > 1 - na\)...
• 18M.1.hl.TZ1.6: Use the principle of mathematical induction to prove...
• 16M.1.hl.TZ2.8: Use mathematical induction to prove that \(n({n^2} + 5)\) is divisible by 6 for...
• 16M.1.hl.TZ1.12b: Use mathematical induction to prove...
• 16N.1.hl.TZ0.13c: Use the principle of mathematical induction to prove...
• 17N.1.hl.TZ0.11b: By using mathematical induction, prove...
• 15N.1.hl.TZ0.8b: Consider \(f(x) = \sin (ax)\) where \(a\) is a constant. Prove by mathematical induction that...
• 15N.3ca.hl.TZ0.3a: Prove by induction that \(n! > {3^n}\), for \(n \ge 7,{\text{ }}n \in \mathbb{Z}\).
• 12M.1.hl.TZ2.13b: Prove by induction that the \({n^{{\text{th}}}}\) derivative of \({(2x + 1)^{ - 1}}\) is...
• 12N.1.hl.TZ0.12b: Let \({F_n}(x) = \frac{x}{{{2^n} - ({2^n} - 1)x}}\), where \(0 \leqslant x \leqslant 1\). Use...
• 08M.1.hl.TZ2.12b: Use mathematical induction to prove that for \(n \in {\mathbb{Z}^ + }\)...
• 11M.2.hl.TZ2.13A: Prove by mathematical induction that, for \(n \in {\mathbb{Z}^ +...
• 09M.1.hl.TZ2.8: Prove by mathematical induction \(\sum\limits_{r = 1}^n {r(r!) = (n + 1)! - 1} \),...
• 09N.1.hl.TZ0.11d: Using mathematical induction, prove...
• SPNone.1.hl.TZ0.12c: Suggest an expression for \({f^{(2n)}}(x)\), \(n \in {\mathbb{Z}^ + }\), and prove your...
• 10M.1.hl.TZ1.13: (a)     Show that...
• 10M.1.hl.TZ2.11: (a)     Consider the following sequence of equations.    ...
• 13M.2.hl.TZ2.8: Use the method of mathematical induction to prove that \({5^{2n}} - 24n - 1\) is divisible by 576...
• 11N.1.hl.TZ0.6: Given that \(y = \frac{1}{{1 - x}}\), use mathematical induction to prove that...
• 14M.2.hl.TZ1.7: Prove, by mathematical induction, that \({7^{8n + 3}} + 2,{\text{ }}n \in \mathbb{N}\), is...
• 14M.2.hl.TZ2.13a: Consider \(z = r(\cos \theta  + {\text{i}}\sin \theta ),{\text{ }}z \in \mathbb{C}\). Use...
• 13N.1.hl.TZ0.6: Prove by mathematical induction that \({n^3} + 11n\) is divisible by 3 for all...
• 15M.1.hl.TZ1.11b: Prove by induction that...
• 15M.1.hl.TZ2.13c: Prove, by mathematical induction, that...
• 14N.1.hl.TZ0.8: Use mathematical induction to prove that...
• 17M.1.hl.TZ2.8: Prove by mathematical induction that...
• 17M.1.hl.TZ1.8: Use the method of mathematical induction to prove that \({4^n} + 15n - 1\) is divisible by 9 for...