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Question

If the sum S=20C2+2.20C3+3.20C4+.....+19.20C20 can be expressed as 1+p.2q, then find the minimum value of (p+q) where p and qϵN.

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Solution

S=20r=1(r1)20Cr
=20r=120Cr20r=120Cr
=2020r=119Cr1(2201)
=20(219)(2201)
=1+(219)(202)
=1+18(219)
p=18
q=19
p+q=37.

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