If , being even the value of is equal…

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

If (1+x)n=C0+C1x+C2x2+C3x3+⋯+Cnxn(1+x)^n = C_0 + C_1 x + C_2 x^2 + C_3 x^3 + \dots + C_n x^n , nn being even the value of C0+(C0+C1)+(C0+C1+C2)+⋯+(C0+C1+C2+⋯+Cn−1)C_0 + (C_0 + C_1) + (C_0 + C_1 + C_2) + \dots + (C_0 + C_1 + C_2 + \dots + C_{n-1}) is equal to (1) n⋅2nn \cdot 2^n (2) n⋅2n−1n \cdot 2^{n-1} (3) n⋅2n−2n \cdot 2^{n-2} (4) n⋅2n−3n \cdot 2^{n-3}

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