Find the first four terms in the binomial expansion of (1+x)^(1/5) and state the range of values of x for which this expansion is valid.Hence approximate (31)^(1/5) correct to four decimal places.

Answer 1

If you are studying this, you must know
(1+x)^n = 1 + nx + n(n-1)(x^2)/2! + ...
valid only for |x| < 1

now let's apply it to your problem of 31^(1/5)

= (32 - 1)^(1/5)
= 32^(1/5)(1 - 1/32)^(1/5)
= 2 (1 - 1/32)^(1/5))
= 2( 1 + (1/5)(-1/32) + (1/5)(-4/5)/2 (-1/32)^2 + (1/5)(-4/5)(-9/5)/6 (-1/32)^3 + .... )
= 2(1 -.00625 + .000078125 - .000001465 + ...)
= 2(.9938266...)
= 1.98765..

using my calculator to find 32^(1/5)
I got 1.98734

Answer 2

Good work, but you had to use a different function. Poorly set problem...