Binomial Theorem – Notes
Binomial Theorem for Positive Integral Indices
The number of terms in an expansion is one more than the power of the binomial.
The coefficients of the first and the last terms of an expansion are both 1.
(x + y)n = nC0xn + nc1xn – 1y + nC2xn – 2y2 +…. + nCn – 1xyn – 1 + nCnyn
nC0, nC1, nC2,… nCn – 1, nCn are called binomial coefficients.
General and Middle Terms
In the expansion (x + y)n
- General term, Tr + 1 = nCrxn – r yr
- Middle term when n is even = ( th term