Show that 24n-15n-1 is divisible by 225 by using binomial theorem.

Dear Student!

24n – 15n – 1

= (24)n – 15n – 1

= 16n –15n – 1

= (1 + 15)n – 15n – 1

= [ nCo +  nC1 (15) + nC2 (15)2 + nC3 (15)3+ ........+ nCn (15)n] – 15n – 1

= [ 1 + 15n + nC2 (15)2 + nC3(15)3 + ....+ nCn (15)n ] – 15n – 1

= nC2 (15)2 + nC3 (15)3 + ...... nCn (15)n

= (15)2 [ nC2 + nC3 (15) + ....+ nCn (15)n – 2 ]

= 225 × A positive integer

∴ 24n – 15n – 1 is divisible by 225.

Cheers!

  • 36
What are you looking for?