CSC_226_Midterm_8

CSC_226_Midterm_8 - 2k nk n 1 k n 1 k 1 P(n + 1) ( + ) + n...

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14. P(n): + + … + + 1k 2k nk nk 1 Domain:{k| k > 0} {n|n > 0} Basis: P(1): 11 12 (True) Proof: + + …+ + 1k 2k nk nk 1 (Inductive Hypothesis) + + … + + + …+ 1k 2k nk nk nk nk + + … + +( + ) ≤( + ) +( + ) + … +( + ) 1k 2k nk n 1 k n 1 k n 1 k n 1 k + + … + + ( + ) ≤( + )( + ) 1k 2k nk n 1 k n 1 n 1 k + + … + +( + ) ≤( + )( + ) 1k
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Unformatted text preview: 2k nk n 1 k n 1 k 1 P(n + 1) ( + ) + n 1 k 1 (mod 101) Binary = 51 5 1 = 52 25 1 = = 54 252 19 = = 58 192 58 1 = = 516 582 31 1 = = 532 312 52 1 = = 564 522 78 1 15. 5 x 25 = 24 (mod 101) 24 x 58 = 79 (mod 101) 79 x 31 = 25 (mod 101) 25 x 52 = 88 (mod 101) 88 x 78 = 97 (mod 101)...
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CSC_226_Midterm_8 - 2k nk n 1 k n 1 k 1 P(n + 1) ( + ) + n...

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