Question Detail

MTH 101 Binomial Expansion Objective Question

Question

In the expansion of (1 - x)^(1/4) up to x^7, evaluate 77^(1/4) correct to five significant figures.
Options
A 3.9306
Correct Answer
B 3.9500
C 3.9255
D 3.9400
Correct Answer

Option A is the correct answer.

Detailed Explanation

Write 77 = 81*(1 - 4/81), expand (1 - x)^(1/4) using binomial theorem, sum up terms → 3.9306

Hint

Factor out a perfect fourth power, use binomial series for small x.

Question Info