(a)using the binomial theorem,expand (x+1)^77.
(b)hence prove that when 81^77 is divided by 100,the remainder is 61.
點解AND 點做
maths m1
2011-09-25 6:43 am
回答 (1)
2011-09-25 7:06 am
✔ 最佳答案
a.(x+1)^77
= Σ(r=0,77) 77Cr x^r
b.
Put x = 80,
81^77= Σ(r=0,77) 77Cr 80^r
For r >= 2, it is divisible by 100,
only when r = 0 and 1, it may not be divisible by 100,
By checking this two term,
Sum of the two term
= 77C0 + 77C1 * 80
= 6161
6161/100
= 61 ... 61
Therefore, the remainder = 61
參考: Hope the solution can help you^^”
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