InterviewSolution
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InterviewSolution
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For any positive integer n, if `4^(n)-3n` is divided by 9, then what is the remainder ?A. 8B. 6C. 4D. 1 |
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Answer» Correct Answer - D Using binomial theorem. `4^(n)-3n=(1+3)^(n)-3n` `=1+n.3+(n(n-1))/(2!)3^(2)+…-3` `=1+(n(n+1))/(2!).3^(2)+(n(n-1)(n-2))/(3!).3^(3)+....` `rArr" "4^(n)-3n=9{(n(n-1))/(2!)+....}+1` Thus, when `4^(n)-3n` is divided by 9, the remainder is 1. |
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