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1. The remainder when 6^{6^{6^{6^{.^{.^∞}}}}} is divided by 10 is :

A. 3

B. 6

C. 5

D. 0

Solution:

\begin{aligned} Since, \\ \frac{6}{10} \to remainder is 6 \\ \frac{6^{6}}{10} \to remainder is 6 \\ \frac{6^{6^{6}}}{10} \to remainder is 6 \\ \frac{6^{6^{6^{6}}}}{10} \to remainder is 6 \\ \frac{6^{6^{6^{6^{6}}}}}{10} \to remainder is 6 and so on . \\ Thus, in all the such cases \\ The remainder will always be 6 \end{aligned}

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