Question

What the coefficient of x² in
(1+x) ²ⁿ
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Answer 1

Let Tr+1Tr+1 be the term containing x2x2.

Tr+1=6Cr(x2)6−r(1x3)rTr+1=6Cr(x2)6−r(1x3)r

=6Crx12−2r1x3r=6Crx12−5r=6Crx12−2r1x3r=6Crx12−5r

As the coefficient of x is 2

12 - 5r = 2 ⇒⇒ r = 2

∴∴ Coefficient of x2=6C2=15x2=6C2=15