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If the coefficients of three consecutive...

If the coefficients of three consecutive terms in the expansion of `(1+x)^n` are in the ratio 1:7:42, then find the value of `ndot`

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Suppose the three consecutive terms in the expansion of `(1+x)^(k)` are `(r-1)^(th),r^(th) and (r+1)^(th)` term.
According to question
Coefficient of `T_(r-1)`: Coefficient of `T_(r)`: Coefficient of `T_(r+1)=1:7:42`, so we have,
`("Coeff. of "T_(r-1))/("Coeff. of "T_(r))=(1)/(7)implies(.^(k)C_(r-2))/(.^(k)C_(r-1))=(1)/(7)impliesk-8r+9=0` . . . . (i)
and `("Coeff. of "T_(r))/("Coeff. of "T_(r+1))=(7)/(42)` i.e., k-7r+1=0 . . . . (ii) ltbRgt Solving (i) and (ii) we get, k=55.
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