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392 Rh Ex. Expand in a series of ascending powers of x.

Dividing x^0, of the first term of the numerator, by x^2, of the first term of the denominator, we obtain x^-2 for the first term of the expansion ; therefore we assume

then 2=2A42Bla+ 2Cla*4+ 2Di\a3+.. 3A 3B 38C

Equating the coefficients of like powers of x, we have

A=1; 2B-3A=0, 2C-3B=0, 2D-3C=0, B=3 2; C=9 4; D = 27 8

thus

EXAMPLES XLII. b.

Expand to four terms in ascending powers of x:

EXPANSION OF SURDS INTO SERIES.

489. Expand 1+x in ascending powers of x.

Let 1+x =A+ Bx + Cx^2 + Dx^3 + Ex^4 + ---.

By squaring both sides of the equation, we have

1+x=A^2+2AB x B^2+ BP P4+2AD +2AC +2BC +2BD +2AE