jc binomial question

ItchyArmpit SG

hihi guys... how to do these binomial question in my tutorial ar?

Find the coefficient of x^6 in the expansion of (4+x^2)^1/2

suppose to be a very easy question.. but i know nothing about finding the terms in binomial.. i only know how to expand with ascending and descending powers.. thanks for any help! thanks!

ItchyArmpit SG

another question i dunno... obtain the binomial expansion of (4-x)^n, where n is not a positive integer, as a series of ascending powers of x up to and including the terms in x^2.

after that, next part of the same question

by putting x = 1/16 and a suitable value of n in your result, find an approximate value for 7^1/2, giving ur answer correct to 2 d.p.

wishboy SG

Find the coefficient of x^6 in the expansion of (4+x^2)^1/2

since the question asked for coefficient of x^6, u should expand in ascending powers

(4+x²)^½
= 2(1+x²/4)^½
= 2[1 + (1/2)(x²/4) + (1/2)(-1/2)/2! * (x²/4)² + (1/2)(-1/2)(-3/2)/3! * (x²/4)³ + ... ]
= 2[... ... + (1/16) * (x^6 / 64) + ... ... ]
= x^6 / 512 + ...

coefficient of x^6 = 1/512