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kq6up
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Homework Statement
4. Write the Maclaurin series for 1/√(1 + x) in ∑ form using the binomial coefficient
notation. Then find a formula for the binomial coefficients in terms of n as we did
in Example 2 above.
Homework Equations
[tex] { \left( 1+x \right) }^{ P }=\sum _{ n=0 }^{ \infty }{ \left( \underset { n }{ P } \right) } { x }^{ n } [/tex]
The Attempt at a Solution
This is what I got, [tex] \frac { 1 }{ \sqrt { (1+x) } } =\sum _{ n=0 }^{ \infty }{ \left( \underset { n }{ -1/2 } \right) } { x }^{ n } [/tex]
This is the book's solution [tex] \left( \overset { -1/2 }{ n } \right) =\frac { { (-1) }^{ n }(2n-1)! }{ (2n)! } [/tex] I am not understanding the whole double factorial.
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