Given that the binomial expansion of (1+kx)^n begins 1+8x+16x^2+... a) find k and n b) for what x is this expansion valid?

a) We compare the expansion given to the standard binomial expansion (remembering the powers of k).(1+kx)n=1+n(kx)+(n(n-1)/2)(kx)2+...As this is true for all x (for which the expansion holds), we can compare coefficients. So nk=8 and k2n(n-1)/2=16 (or k2n(n-1)=32).Then we can solve these simultaneous equations by substitution. Rearrange the first equation to obtain k=8/n. Then substitute this into the second equation to obtain (8/n)2n(n-1)=32. Rearrange to obtain 2(n-1)/n=1, and then obtain n=2. Substitute this into k=8/n to get k=4.b) Now we require |kx|<1 for the expansion to hold, and as we now know k=4, we must have |x|<1/4.

GC
Answered by George C. Maths tutor

4865 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

y=e^2x-11e^x+24 Find the stationary point, nature of the stationary point, the x-intercepts and the y-intercept (calculator allowed)


Differentiate y= (2x+1)^3. [The chain rule]


Find the area between the curve y = 8 + 2x - x^2 and the line y = 8 - 2x.


Problem of Optimisation: A company is designing a logo. The logo is a circle of radius 4 inches with an inscribed rectangle. The rectangle must be as large as possible.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences