+0  
 
0
28
1
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(a) Simplify (n/k)/(n/(k - 1))

 

(b) For some positive integer n, the expansion of (1 + x)^n has three consecutive coefficients a, b, c that satisfy 1:8:28.   What must n be?

 Jan 6, 2023
 #1
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b)

 

Suppose the coefficients are:  (n / r−1), (n / r), (n / r+1). 


Then [n−r+1] / r =8 : 1,
[n−r] / [r+1] =28 : 8, solve for n, r


n ==8  and r ==1
Expand  (x + 1)^8 ==x^8 + 8 x^7 + 28 x^6 + 56 x^5 + 70 x^4 + 56 x^3 + 28 x^2 + 8 x + 1
 

So, the first 3 coefficients are: 1 : 8 : 28

 Jan 7, 2023

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