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2. (a) Show that for all integers n ≥ 0,32n-1 is divisible by 8. (b) Show that 2n< (n+2)! for all integers n 20.. (c) Show that 1 + nx < (1+x)", for all for all integers n ≥ 2, here x > -1. (d) Show that √<++¨¨¨+; for all integers n 22. +

2. (a) Show that for all integers n ≥ 0,32n-1 is divisible by 8. (b) Show that 2n< (n+2)! for all integers n 20.. (c) Show that 1 + nx < (1+x)", for all for all integers n ≥ 2, here x > -1. (d) Show that √<++¨¨¨+; for all integers n 22. +

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. (a) Show that for all integers n ≥ 0,32m - 1 is divisible by 8. (b) Show that 2n< (n + 2)! for all integers n > 0.. (c) Show that 1 + nx < (1 + x)", for all for all integers n ≥ 2, here x > -1. (d) Show that √n<++´ for all integers n ≥ 2. + 1 √
Transcribed Image Text:2. (a) Show that for all integers n ≥ 0,32m - 1 is divisible by 8. (b) Show that 2n< (n + 2)! for all integers n > 0.. (c) Show that 1 + nx < (1 + x)", for all for all integers n ≥ 2, here x > -1. (d) Show that √n<++´ for all integers n ≥ 2. + 1 √
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