7n-3n is a divisible by 4. 

please solve this

it can be prvd byP.M.I.

for n=1

7n-3n=7-3=4 which is div. by 4

so true fr n=1

now,

let it be true for n=k

then,

7k-3k=4m 

7k=4m+3k...........(1)

now, for n=k+1

prove it for n=k

pt. 7k+1-3k+1 is divisible by 4

now,7k+1-3k+1=7.7k-3k+1

=7(4m+3k)-3k+1.........from eq.1

=7.4m+7.3k-3.3k

=7.4m+3k(7-3)

=7.4m+3k.4

=4(7m+3k)+0

since remainder =0

so it is divisible by 4

so tru for n=k+1

so

by p.m.i. it is tru for any valueof(n=natural no.)

  • 19

put n=1

the 7-3=4 which is divisible by 4

now n=2

=>72-32=49-9=40

result is true for n=2 as it is divisible by 4 so 7n-3n is divible by 4 as result will be tru for any value of (n=natural no.)

  • -12
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