What are the Important Formulas in Chapter 8 Binomial Theorem?
Answer (1)
Here are some important formulae of the Binomial Theorem:
1. Binomial Expansion Formula:(a + b)^n = Σ (from r = 0 to n) [nCr * a^(n - r) * b^r]
2. Binomial Coefficient: The binomial coefficient nCr is given by: nCr = n! / (r!(n - r)!)
where n! is the factorial of n.
3. Middle Term (When n is Even): If n is even, the middle term of the expansion is the term with r=n/2.
4. Odd n Middle Terms: If n is odd, the two middle terms are the terms corresponding to r=n/2 and r=n/2+1
5. Sum of All Terms: The sum of all the terms in the binomial expansion of (a+b)^n is given by:(a + b)^n = a^n + nC1 * a^(n-1) * b + nC2 * a^(n-2) * b^2 + ... + b^n
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