General Term, Middle Term and Greatest Term

General Term, Middle Term and Greatest Term

This lesson covers the following key concepts:

• General term Tr+1 in binomial expansion
• Finding coefficient of specific term
• Middle term when n is even and odd
• Greatest binomial coefficient
• Greatest term in numerical expansion
• Ratio of consecutive terms
• Independent term (constant term)

Important Formulas

• $$T_{r+1} = ^nC_r x^{n-r} y^r \text{ (general term)}$$
• $$\text{Middle term (n even): } T_{n/2 + 1}$$
• $$\text{Middle terms (n odd): } T_{(n+1)/2}, T_{(n+3)/2}$$
• $$\text{Greatest coefficient: } ^nC_{n/2} \text{ (n even)}$$
• $$\frac{T_{r+1}}{T_r} = \frac{(n-r+1)}{r} \cdot \frac{y}{x}$$
• $$\text{For greatest term: } T_r \geq T_{r-1} \text{ and } T_r \geq T_{r+1}$$