If a,b,c....

If a,b,c be the three consecutive coefficients in the expansion of a power of (1+x),
prove that the index of the power is

2ac + b(a+c)b² - ac

1 Answers

we know that

a= ⁿC_r-1
b= ⁿC_r
c= ⁿC_r+1

numerator is ac+ab + ac+bc
which is a(b+c) + c(a+b)

a+ b = ⁿ⁺¹C_r
b+c = ⁿ⁺¹C_r+1

Now can you complete this problem yourself?

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