Calculate the sum of the coefficients of the expansion terms (a + b) 7?

1.The nth power of a binomial is expressed by the expansion of the Newton binomial:

(a + b) ^ n = Σ [i = 0; n] (C (n, i) * a ^ i * b ^ (n – i)), where
C (n, i) = n! / (I! * (N – i)!) – binomial coefficients.
2. The value of the function f (a, b) = (a + b) ^ n at the point (a; b) = (1; 1) is equal to the sum of all binomial coefficients:

f (1; 1) = Σ [i = 0; n] (C (n, i) * 1 ^ i * 1 ^ (n – i)) = Σ [i = 0; n] (C (n, i)).

3.On the other hand, it is equal to:

f (1; 1) = (1 + 1) ^ n = 2 ^ n.

Therefore, the sum of the coefficients:

Σ [i = 0; n] (C (n, i)) = 2 ^ n.

4. For n = 7 we get:

Σ [i = 0; 7] (C (7, i)) = 2 ^ 7 = 128.

Answer: 128.