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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..