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Let C0, C1, C2,..., C15 denote the binomial coefficients in the expansion of (1 + x)¹⁵. Then the value of C1/C0 + C2/C1 + C3/C2 +... + C15/C14 is:

1. 60
2. 120
3. 64
4. 124

Correct answer: 120

Solution

Since Ck/C(k-1) = (n-k+1)/k, the term k*(Ck/C(k-1)) = n-k+1. Summing k=1..15 gives sum of (16-k) = 15+14+...+1 = 15*16/2 = 120.

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