Archive
17th of March 2017
Mathematics
Q:

Show that 9^n+1-8n-9 is divisible by 64

Reemali Patil - CBSE - Class XI Science

Friday, March 17, 2017 at 17:25:PM

A:

begin mathsize 16px style 9 to the power of straight n plus 1 end exponent minus 8 straight n minus 9
equals open parentheses 1 plus 8 close parentheses to the power of straight n plus 1 end exponent minus 8 straight n minus 9
open parentheses straight C presuperscript straight n plus 1 end presuperscript subscript 0 plus straight C presuperscript straight n plus 1 end presuperscript subscript 1 8 to the power of 1 plus straight C presuperscript straight n plus 1 end presuperscript subscript 2 8 squared plus..... plus straight C presuperscript straight n plus 1 end presuperscript subscript straight n plus 1 end subscript 8 to the power of straight n plus 1 end exponent close parentheses minus 8 straight n minus 9
equals open square brackets 1 plus 8 left parenthesis straight n plus 1 right parenthesis plus 64 straight C presuperscript straight n plus 1 end presuperscript subscript 2 plus...... plus 64 left parenthesis 8 right parenthesis to the power of straight n minus 1 end exponent close square brackets minus 8 straight n minus 9
equals open square brackets 1 plus 8 straight n plus 8 plus 64 straight C presuperscript straight n plus 1 end presuperscript subscript 2 plus...... plus 64 left parenthesis 8 right parenthesis to the power of straight n minus 1 end exponent close square brackets minus 8 straight n minus 9
equals open square brackets 8 straight n plus 9 plus 64 straight C presuperscript straight n plus 1 end presuperscript subscript 2 plus...... plus 64 left parenthesis 8 right parenthesis to the power of straight n minus 1 end exponent close square brackets minus 8 straight n minus 9
equals 8 straight n plus 9 plus 64 open parentheses straight C presuperscript straight n plus 1 end presuperscript subscript 2 plus...... plus 8 to the power of straight n minus 1 end exponent close parentheses minus 8 straight n minus 9
equals 64 open parentheses straight C presuperscript straight n plus 1 end presuperscript subscript 2 plus...... plus 8 to the power of straight n minus 1 end exponent close parentheses
Hence comma space 9 to the power of straight n plus 1 end exponent minus 8 straight n minus 9 space is space divided space by space 64.
end style

Friday, March 17, 2017 at 17:43:PM