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SOLUTION SET FOR THE HOMEWORK PROBLEMS Page 5 Problem 8 Prove that if x and y are real numbers, then 2xy ≤ x2 y2 Proof First we prove that if.
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Homework 1 Solutions Math 171, Spring 10 Please send corrections to henrya@mathstanfordedu 22 Let h X!Y, g Y !Z, and f Z!W Prove that (f g) h= f (g h). Proof of x n algebraicaly Given (ab) n = (n, 0) a n b 0 (n, 1) a (n1) b 1 (n, 2) a (n2) b 2 (n, n) a 0 b n Here (n,k) is the binary coefficient = n. PK U›£R¸ÿÜ)6 o ;.
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A combination takes the number of ways to make an ordered list of n elements (n!), shortens the list to exactly x elements ( by dividing this number by (nx)!. D f f Z gY Qx '~1Ix7 (v F X y a # ,># I x _ Yldx 3 & ~ x KV, q zQ'98L 1. Memoires_du_apoleon_Tome_7`$üŽ`$ü BOOKMOBI — K ¨T 7ó A$ J Rà Ô d¡ mš v S ˆ$ µ ™Ó ¢Ë «™ ´ ½ "Æ $Îú&Ø (á *éÀ,ó ü)0 r2 4 ‹6 n8 )> 2 ;.
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