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49^n+16 n-1 is divisble by

Option: 1

3


Option: 2

19


Option: 3

64


Option: 4

29


Answers (1)

best_answer

\begin{aligned} & 49^n+16 n-1=(1+48)^n+16 n-1 \\ & 1+{ }^n C_1(48)+{ }^n C_2(48)^2+\ldots+{ }^n C_n(48)^n+16 n-1 \\ = & (48 n+16 n)+{ }^n C_2(48)^2+{ }^n C_3(48)^3+\ldots+{ }^n C_n(48)^n \\ = & 64 n+8^2\left[{ }^n C_2 \cdot 6^2+{ }^n C_3 \cdot 6^3 \cdot 8+{ }^n C_4 \cdot 6^4 \cdot 8^2+\ldots+{ }^n C_n \cdot 6^n \cdot 8^{n-2}\right] \end{aligned}

Hence, 49^n+16 n-1 is divisible by 64.

Posted by

jitender.kumar

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