標題:
發問:
1a) Using the binomial theorem, expand (x+1)^77 b) Hence prove that when 88^77 is divided by 100, the remainder in 61 2 ) Using the binomial theorem, find the remainder when 8^88 is divided by each of the following integers. a) 7 b) 49 更新: 更正： 1a) Using the binomial theorem, expand (x+1)^77 b) Hence prove that when 81^77 is divided by 100, the remainder in 61
最佳解答:
88^77為偶數,除以100,餘數61為奇數???? 2010-02-22 22:15:14 補充： 1. (a) (x+1)^77=C(77,0)+C(77,1)x+C(77,2)x^2+...+C(77,77)x^77 =1+77x+x^2*(....) (b) 81^77=(80+1)^77 =1+77*80+80^2*(.....) =6161+ 100*(...) so that 81^77 is divided by 100 obtained the remainder 61 2. 8^88=(7+1)^88= 1+88*7+7^2*(....) = 1+ 616+ 49*(...) (a) 8^88 is divided by 7 the remainder is 1 (b) 1+616 divded by 49 the remainder is 29
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F.4 Binomial Theorem發問:
1a) Using the binomial theorem, expand (x+1)^77 b) Hence prove that when 88^77 is divided by 100, the remainder in 61 2 ) Using the binomial theorem, find the remainder when 8^88 is divided by each of the following integers. a) 7 b) 49 更新: 更正： 1a) Using the binomial theorem, expand (x+1)^77 b) Hence prove that when 81^77 is divided by 100, the remainder in 61
最佳解答:
88^77為偶數,除以100,餘數61為奇數???? 2010-02-22 22:15:14 補充： 1. (a) (x+1)^77=C(77,0)+C(77,1)x+C(77,2)x^2+...+C(77,77)x^77 =1+77x+x^2*(....) (b) 81^77=(80+1)^77 =1+77*80+80^2*(.....) =6161+ 100*(...) so that 81^77 is divided by 100 obtained the remainder 61 2. 8^88=(7+1)^88= 1+88*7+7^2*(....) = 1+ 616+ 49*(...) (a) 8^88 is divided by 7 the remainder is 1 (b) 1+616 divded by 49 the remainder is 29
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