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Sum of binomial coefficients of odd numbered terms

In the expans...

Question

In the expansion of $(a + b + c)^{s}$ find (1) the number of terms, (2) the sum of the coefficients of the terms.

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Solution

$(a + b + c)^{8}$
n = 8 , r =number of independent terms in bracket = 3

number of terms = $C_{r - 1}^{n + r - 1} = C_{2}^{10} = 45$

sum of coefficients = $r^{n}$

$= 3^{8} = 6561$

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Sum of binomial coefficients of odd numbered terms

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