- #1
hangainlover
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Homework Statement
Maclaurin series for square root (1+x)
Homework Equations
The Attempt at a Solution
I attempted to find the maclaurin series for the function Square root of 1+x.
F(0)=1 first term= 1
F'(0)=1/2 second term= (1/2)x
F''(0)=-1/4 Third term (-1/4)x^2
F'''(0)=3/8 fourth term (3/8*3!) x^3
F''''(0)=15/16 fifth (-15/16*4!) x^4
F'''''(0)105/32 six (105/32*5!) x^5
Therefore,
f(x)= 1+ (1/2)x + (-1/4)x^2 + (3/8*3!) x^3 + (-15/16*4!) x^4 + (105/32*5!) x^5
The problem is to find generalize term .
I have ( ((-1)^(n-1)) * something *x^n) / ((2^n) * (n!))
I cannot find that "something". because it exists as 1 for the first, second, and the third term , but then it increases to 3,15, 105
so the previous term increases by factor of 3,5,7... (somewhat recursive?)
Help..