Question
Apply the binomial theorem to find the first three terms in ascending powers of x of (1 + x)ⁿ, where n=32
Answers
for any n, we have
(1+x)^n = 1^n + n*1^(n-1)x + n(n-1)/2 1^(n-2)x^2 + ...
= 1 + nx + n(n-1)/2 x^2 + ...
So, plug in n=32
(1+x)^n = 1^n + n*1^(n-1)x + n(n-1)/2 1^(n-2)x^2 + ...
= 1 + nx + n(n-1)/2 x^2 + ...
So, plug in n=32
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