Important expansions:

• (1+ x)^-1 = 1- x +x² -x³ + . . . + (-1)^rx^r+. . .
• (1 - x)^-1 = 1+ x +x² +x³ + . . .+ x^r + . . .
• (1+ x)^-2 = 1- 2x +3x² -4x³+ . . .+ (-1)^r(r+1)x^r+. . .
• (1 - x)^-2 = 1+ 2x +3x² +4x³ + . . .+ (r+1)x^r+. . .
• (1+x)^-3 = 1- 3x +6x² -10x³ +. . .+ (-1)^r   x^r+. . .
• (1-x)^-3 = 1+ 3x +6x² +10x³ + . . .+   x^r+. . .
• In general coefficient of x^r in (1 - x)^{- n} is ^{n + r -1}C_r .
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