Show that  is divisible by 64, whenever n is a positive integer:

Asked by Topperlearning User | 30th Sep, 2016, 09:29: PM

Expert Answer:

9 to the power of n plus 1 end exponent minus 8 n minus 9 equals 9 left parenthesis 1 plus 8 right parenthesis to the power of n minus 8 n minus 9

9 left parenthesis 1 plus 8 n plus C presuperscript n subscript 2 8 squared plus..... plus C presuperscript n subscript n 8 to the power of n right parenthesis minus 8 n minus 9
9 plus 72 n plus 64 x 9 left parenthesis C presuperscript n subscript 2 plus C presuperscript n subscript 3 8 plus C presuperscript n subscript 4 8 squared plus... plus C presuperscript n subscript n 8 to the power of n minus 2 end exponent right parenthesis minus 8 n minus 9
64 n plus 64 x 9 left parenthesis C presuperscript n subscript 2 plus C presuperscript n subscript 3 8 plus C presuperscript n subscript 4 8 squared plus... plus C presuperscript n subscript n 8 to the power of n minus 2 end exponent right parenthesis space w h i c h space i s space d i v i s i b l e space b y space 64
Hence,  is divisible by 64.

Answered by  | 30th Sep, 2016, 11:29: PM