any 3 successive coefficient in the expansion of (1+x)^n where n is a positive integer are 28,56,70 then n is
Let the terms be nCr , nCr+1 , nCr+2
Now, nCr+1 /nCr = (n - r) / (r + 1) = 56 / 28 = 2
After cross multiplying
= n = 3r + 2 = 4n = 12r + 8 ---------- (i)
Now,
nCr+2 /nCr+1 = 70 / 56
= (n - r - 1) / (r + 2) = 5 / 4
= After cross multiplying,
4n = 9r + 14----------(ii)
Equating (i) and (ii)
9r + 14 = 12r + 8
3r = 6
r = 2
Applying the value of r in (i)
4n = 12 * 2 + 8
4n = 24 + 8 = 32
n = 8
Hence, n = 8
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