I. Induction a. 1 + 2 + 2² +: · +2" = 2n+1 _ 1, for all nonnegative integers n.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Final Exam Review
I. Induction
a. 1 + 2 + 22 + . +2" = 2n+1_ 1, for all
nonnegative integers n.
b. n³ – n is divisible by 3,
for n> 0
1! + 2· 2!+· · +n•n! = (n + 1)! –
c. Prove that 1
1 whenever n is a positive integer
d. Prove that 6 divides n³
nonnegative integer.
n whenever n is a
Transcribed Image Text:Final Exam Review I. Induction a. 1 + 2 + 22 + . +2" = 2n+1_ 1, for all nonnegative integers n. b. n³ – n is divisible by 3, for n> 0 1! + 2· 2!+· · +n•n! = (n + 1)! – c. Prove that 1 1 whenever n is a positive integer d. Prove that 6 divides n³ nonnegative integer. n whenever n is a
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