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

Asked by Reemali 17th March 2017, 5:25 PM
Answered by Expert
Answer:

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

Answered by Expert 17th March 2017, 5:43 PM
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