Binomial Theorem
Binomial Theorem
nta_abhyas_2025
Grade 11
Question:
If $C_0, C_1, C_2, \ldots, C_n$ are binomial coefficients, (where $C_r = ^nC_r$), then the value of $C_0 - C_1 + C_2 - C_3 + \ldots + (-1)^n C_n$ is equal to
Step-by-Step Solution
Key Concept: Substituting specific values of $x$ in the binomial expansion helps find sums of alternating binomial coefficients
Put $x = -1$ in the binomial expansion $(1+x)^n = C_0 + C_1x + C_2x^2 + \ldots + C_nx^n$. This gives $(1-1)^n = C_0 - C_1 + C_2 - C_3 + \ldots + (-1)^n C_n = 0^n = 0$.
Correct Answer: 3