(19:56) gp > 2+2  \\ basic (and \\ is the "comment to end of line" character sequence)
%1 = 4
(19:56) gp > 100! \\ not as basic
%2 = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000
(19:57) gp > 1/(1-x) \\ try to make a power series
%3 = -1/(x - 1)      \\ oops, too smart, gp treats rational functions as exact expressions
(19:57) gp > 1/(1-x)+O(x^10)  \\ coerce it into a power series
%4 = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + O(x^10)
(19:57) gp > taylor(1/(1-x),x) \\ another way: explicitly ask for taylor series
%5 = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12 + x^13 + x^14 + x^15 + O(x^16)
(19:57) gp > ?  \\ type ? to get help
Help topics: for a list of relevant subtopics, type ?n for n in
   0: user-defined functions (aliases, installed and user functions)
   1: PROGRAMMING under GP
   2: Standard monadic or dyadic OPERATORS
   3: CONVERSIONS and similar elementary functions
   4: functions related to COMBINATORICS
   5: NUMBER THEORETICAL functions
   6: POLYNOMIALS and power series
   7: Vectors, matrices, LINEAR ALGEBRA and sets
   8: TRANSCENDENTAL functions
   9: SUMS, products, integrals and similar functions
  10: General NUMBER FIELDS
  11: Associative and central simple ALGEBRAS
  12: ELLIPTIC CURVES
  13: L-FUNCTIONS
  14: HYPERGEOMETRIC MOTIVES
  15: MODULAR FORMS
  16: MODULAR SYMBOLS
  17: GRAPHIC functions
  18: The PARI community
Also:
  ? functionname (short on-line help)
  ?\             (keyboard shortcuts)
  ?.             (member functions)
Extended help (if available):
  ??             (opens the full user's manual in a dvi previewer)
  ??  tutorial / refcard / libpari (tutorial/reference card/libpari manual)
  ??  refcard-ell (or -lfun/-mf/-nf: specialized reference card)
  ??  keyword    (long help text about "keyword" from the user's manual)
  ??? keyword    (a propos: list of related functions).
(19:57) gp > ?4  \\ look at section 4

bernfrac      bernpol       bernreal      bernvec       binomial      eulerfrac     eulerianpol   eulerpol      eulerreal     eulervec      fibonacci     hammingweight
harmonic      numbpart      numtoperm     partitions    permcycles    permorder     permsign      permtonum     stirling      

(19:57) gp > ?numbpart
numbpart(n): number of partitions of n.

(19:58) gp > sum(i=0,10,numbpart(i)*x^i)+O(x^11)  \\ OGF of partitions
%6 = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 11*x^6 + 15*x^7 + 22*x^8 + 30*x^9 + 42*x^10 + O(x^11)
(19:58) gp > prod(i=1,10,1/(1-x^i)+O(x^11))  \\ Euler's formula for the same
%7 = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 11*x^6 + 15*x^7 + 22*x^8 + 30*x^9 + 42*x^10 + O(x^11)
(19:59) gp > %6-%7  \\ check if they match
%8 = O(x^11)    \\ they do, to the desired accuracy
(19:59) gp > quit  \\ all done