Module 6 · Modern Mathematics
Chapter 55: Binomial Theorem
Modern Mathematics
4 topics
What this chapter covers
The 4 topics below make up Binomial Theorem on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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Formula Reference Sheet
This chapter
Expansion & general term
| Binomial expansion | (a+b)ⁿ = Σ nCr · a^(n−r) · b^r, r = 0…n |
|---|---|
| General term | T(r+1) = nCr · a^(n−r) · b^r |
| Number of terms | (a+b)ⁿ has (n+1) terms |
| Binomial coefficient | nCr = n! / [r!(n−r)!] |
| Symmetry of coefficients | nCr = nC(n−r) |
Middle term, sums & special cases
| Middle term (n even) | single term T(n/2 + 1) |
|---|---|
| Middle terms (n odd) | two terms T((n+1)/2) and T((n+3)/2) |
| Sum of all coefficients | put each variable = 1 ⇒ (sum of bases)ⁿ |
| Sum of binomial coefficients | nC0 + nC1 + … + nCn = 2ⁿ |
| Greatest coefficient | the middle coefficient: nC(n/2) (n even) |
CAT reference
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