For which positive integers n is n+6 (n2 -8n)16 Prove your answe.pdf
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Apr. 2, 2023•0 likes•6 views
For which positive integers n is n+6 (n2 -8n)16 Prove your answe.pdf
Apr. 2, 2023•0 likes•6 views
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For which positive integers n is n+6 < (n2 -8n)/16? Prove your answer using mathematical induction. Solution n + 6 < (n² -8n) / 16 16(n + 6) < n² - 8n 16n + 96 < n² - 8n n² - 8n - 16n - 96 < 0 n² -24n- 96 < 0 n² - 24n < 96 n² - 24n + 36 < 96 + 36 (n - 6)² < 132 n - 6 < 132 n - 6 < ± 11.5 n < 6 ± 11.5 If n < 6 + 11.5, n < 17.5 If n < 6 - 11.5, n < - 5.5 Given Domain: n > 0, so 0 < n < 17.5 ¯¯¯¯¯¯¯¯¯¯¯.
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For which positive integers n is n+6 (n2 -8n)16 Prove your answe.pdf
- 1. For which positive integers n is n+6 < (n2 -8n)/16? Prove your answer using mathematical induction. Solution n + 6 < (n² -8n) / 16 16(n + 6) < n² - 8n 16n + 96 < n² - 8n n² - 8n - 16n - 96 < 0 n² -24n- 96 < 0 n² - 24n < 96 n² - 24n + 36 < 96 + 36 (n - 6)² < 132 n - 6 < 132 n - 6 < ± 11.5 n < 6 ± 11.5 If n < 6 + 11.5, n < 17.5 If n < 6 - 11.5, n < - 5.5 Given Domain: n > 0, so 0 < n < 17.5 ¯¯¯¯¯¯¯¯¯¯¯