二项式定理证明题证明32n+2-8n-9 (n为自然数)可被64整除.

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二项式定理证明题证明32n+2-8n-9 (n为自然数)可被64整除.

二项式定理证明题证明32n+2-8n-9 (n为自然数)可被64整除.
二项式定理证明题
证明32n+2-8n-9 (n为自然数)可被64整除.

二项式定理证明题证明32n+2-8n-9 (n为自然数)可被64整除.
证明:32n+2-8n-9=9n+1-8n-9=(8+1)n+1-8n-9
=8n+1+Cn+11•8n++Cn+1n•8+1-8n-9
=8n+1+Cn+11•8n++Cn+1n-1•82
=82(8n-1+Cn+11•8n-2++Cn+1n-1)
∵8n-1+Cn+11•8n-2++Cn+1n-1是整数,
∴32n+2-8n-9能被64整除.