Determine the first three terms in the expansion (x+1x)40
Recall that the Binomial Theorem is defined as
Substituting a=x and b=1x gives the first three terms are
(400)(x)40,(401)(x)39(1x),(401)(x)38(1x)2
From the 40th row of the Pascal's Triangle, we obtain that
(400)=40!0!(40−0)!=1(401)=40!1!(40−1)!=40(402)=40!2!(40−2)!=780
Thus, the first three terms are
=(1)(x)40,(40)(x)39(1x),(780)(x)38(1x)2=x40,40x38,,780x36
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