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ALGEBRA
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399
To find the coefficient of x^r;
(1) If r is even, the coefficient of x^r in the second series is 4(-1)^{r 2}; therefore in the expansion the coefficient of x^r is 3+4(-1)^{r 2}.
(2) If r is odd, the coefficient of x^r in the second series is -3(-1)^{{r-1}{2}} , and the required coefficient is 3(-1)^{{r-1}{2}}- 3.
EXAMPLES XLII. e.
Resolve into partial fractions :
Find the general term of the following expressions when expanded
in ascending powers of x.
