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July 30, 2016
Posted by **louise** on Sunday, July 31, 2011 at 2:46am.

- math -
**MathMate**, Sunday, July 31, 2011 at 7:56amUse the binomial theorem,

(X+Y)^n

=(n,0)X^n+(n,1)X^(n-1)Y+....+(n,n-1)XY^(n-1)+(n,n)Y^n

where

(n,i) is the binomial coefficient

=n!/[(n-i)!i!]

For

n=5,

X=1/a

Y=sqrt(a)

we get

(1/a+sqrt(a))^5

=1/a^5 + (5/a^4)sqrt(a) + (10/a^3)a + (10/a^2)a^(3/2) + (5/a)a^2 + a^(5/2)

which simplifies to

1/a^5 + (5/a^(7/2) + 10/a^2 + 10/sqrt(a) + 5a + a^(5/2)