itiL s 528 || ProveHak Lo

1.	itiL s 528 \|\| ProveHak Lo
Answer» 2.7^n+ 3.5^n-5 is divisible by 24---- to prove put n=1 14+15-4=24 p(1) true. put n=k 2.7^k+ 3.5^k-5=24m-------1) to prove: n=k+1 is true put n= k+1 2.7.7^k+3.5.5^k-5 from 1) -5=24m-2.7^k-3.5^k 14.7^k+15.5^k+24m-2.7^k-3.5^k 24m+7^k(14-2)+5^k(15-03) 24m+12.7^k+12.5^k 24(m+7^k/2+5^k/2) 24 multiplied by any digit means it is divisible by 24. by p.m.i. it is proved that n is true for N Was this answer helpful

Answer»

2.7^n+ 3.5^n-5 is divisible by 24---- to prove

put n=1

14+15-4=24

p(1) true.

put n=k

2.7^k+ 3.5^k-5=24m-------1)

to prove: n=k+1 is true

put n= k+1

2.7.7^k+3.5.5^k-5

from 1) -5=24m-2.7^k-3.5^k

14.7^k+15.5^k+24m-2.7^k-3.5^k

24m+7^k(14-2)+5^k(15-03)

24m+12.7^k+12.5^k

24(m+7^k/2+5^k/2)

24 multiplied by any digit means it is divisible by 24.

by p.m.i. it is proved that n is true for N

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