Quick Recap — Coefficients & Middle Terms

  • Middle term: for even nn, the (n2+1)\big(\tfrac n2+1\big)th term; for odd nn, two middle terms.
  • Sum of coefficients of a polynomial == its value at x=1x=1.
  • The greatest binomial coefficient in (1+x)n(1+x)^n is the central one, nCn/2^nC_{n/2} (or nC(n±1)/2^nC_{(n\pm1)/2}).
  • Coefficients equidistant from the ends are equal: nCr=nCnr^nC_r={}^nC_{n-r}.