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(1+x)n=nC0x0+ nC1x1+ nC2x2+ nC3x3+………………….+ nCnxn-1+ nCnxn
Put x=4
5n= nC040+ nC141+ nC242+ nC343+………………….+ nCn4n-1+ nCn4n
5n=nC040+4{ nC1+ nC24+ nC342+………………….+ nCn4n-2+ 4n-1}
4{ nC1+ nC24+ nC342+………………….+ nCn4n-2+ 4n-1}=5n-1
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