Question

Σ nCr 4r, r ∈ [r=0, n] = .....

(a) 4n

(b) 5n

(c) 4-n

(d) 5-n

Answer 1

Correct option: (b) 5n

Explanation:

To find: n∑r=0 nCr 4r

we know, (1 + x)n = n∑r=0 nCr xr

put x = 4 we get

(1 + 4)n = n∑r=0 nCr 4r

∴ n∑r=0 nCr rn = 5n