Question

Obtain the first five terms of the expansion of (1-1/2x)^7?

Answer 1

See below:

Explanation:

We can use the binomial expansion to find the terms (I'm assuming the second term is `-1/2x` and not `-1/(2x)`):

`(a+b)^n=(C_(n,0))a^nb^0+(C_(n,1))a^(n-1)b^1+...+(C_(n,n))a^0b^n`

First 5 terms are therefore:

• `((7),(0)) (1)^7(-1/2x)^0=1`
• `((7),(1)) (1)^6(-1/2x)^1=-7/2x`
• `((7),(2)) (1)^5(-1/2x)^2=21xxx^2/4=(21x^2)/4`
• `((7),(3)) (1)^4(-1/2x)^3=35xx-x^3/8=-(35x^3)/8`
• `((7),(4)) (1)^3(-1/2x)^4=35xxx^4/16=(35x^4)/16`