a. Write down the first three terms in the binomial expansion of (1-2x)^(1/2) in ascending powers of x. b. Write down the first three terms in the binomial expansion of (1+x)^(-1/2) in ascending powers of x. c. Use your answers to a and b to prove that √(1-2x)(1+x)=1-3/2x+3/8x^2+.....
Added by Kelly B.
Step 1
The binomial expansion of (1-2x)^(1)/(2) is: (1-2x)^(1)/(2) = C(1,0)1^(1-0)(-2x)^0 + C(1,1)1^(1-1)(-2x)^1/2 + C(1,2)1^(1-2)(-2x)^2/2^2 + ... where C(n,r) is the binomial coefficient, which is equal to n!/(r!(n-r)!). So the first three terms Show more…
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