If A=(4n=3n-1,nen) and B=(9n-9,nen) then find A union B and A intersection B
If A=(4n=3n-1,nen) and B=(9n-9,nen) then find A union B and A intersection B
Aleem , 5 Years ago
Grade 10
Magical Mathematics[Interesting Approach]> If A=(4n=3n-1,nen) and B=(9n-9,nen) then ...
1 Answers
Arun
Last Activity: 5 Years ago
4n=(3+1)n = nC0 + nC1*31 + nC2 * 32 + nC3 * 33 +........+ nCn * 3n,
Take nC0 and nC1*3 on left hand side,
x=nC2 *9 + nC3*27...... + nCn *3n,
hence x is always divisible by 9,
So you can write x= 9*(nC2 + nC3*3......+ nCn *3n-2) = 9*z, where z is an integer,
z will only have specific integer values. Hence zUN = N, or XUY=Y
Take nC0 and nC1*3 on left hand side,
x=nC2 *9 + nC3*27...... + nCn *3n,
hence x is always divisible by 9,
So you can write x= 9*(nC2 + nC3*3......+ nCn *3n-2) = 9*z, where z is an integer,
z will only have specific integer values. Hence zUN = N, or XUY=Y
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