General term and middle terms
Sequences, series and the binomial theorem · Mathematics
Study notes
Q: Find (a) the middle term of (x + 2)^4 (b) the term independent of x in (x + 1/x)^6. (a) n = 4 (even): middle is T(3) = C(4,2)x^2(2^2) = 6x^2 x 4 = 24x^2. (b) T(r+1) = C(6,r) x^(6-r)(1/x)^r = C(6,r) x^(6-2r). Set 6-2r = 0: r = 3. Term = C(6,3) = 20.