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**Question - **Math 324 Assignment 1 (due September 17)
Please remember to staple your assignment a nd to write the names of other students you
may have worked with.
1. (1.1 #6)( 5) Show that every non-empty subset X of the set of negative integers has a
greatest element.
2. (1.2 #22)( 5) Use the identity 1/(k2 âˆ’ 1) = ( 1/2 ) (1/(k âˆ’ 1) âˆ’ 1/(k + 1)) to evaluate the
sum âˆ‘
2 â‰¤ k â‰¤ n 1/(k2 âˆ’ 1).
3. (1.3 #22)( 5) Show by mathematical induction that if h > âˆ’ 1 then (1 + h)n â‰¥ 1 + nh for
all non-negative integers n.
4. (1.5 #38)( 5) Show that the square of every odd integer is of the form 8k + 1.
5. (3 + 3 + 4 ) Define an L-number to be a positive integer of the form 3k +
...Read More

**Solution Preview - **x âˆˆ X} is a non-empty subset so has a least element s. Then s = âˆ’ g
with g âˆˆ X and âˆ’ x â‰¥ s = âˆ’ g implies that x â‰¤ g for all x âˆˆ X. Thus g is the greatest
element in X.
2. Our sum âˆ‘ 2 â‰¤ k â‰¤ n 1/(k2 âˆ’ 1) equals (1/2) âˆ‘ 2 â‰¤ k â‰¤ n (1/(k âˆ’ 1) âˆ’ 1/(k + 1)) =
(1/2)( âˆ‘ 2 â‰¤ k

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