The remainder when $10^{10} + 10^{100} + 10^{1000} + . . . . + 10^{10000000000} i s d i v i d e d b y 7$ is

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Solution

The correct option is C 5
The remainder of $(10^{10} + 10^{100} + 10^{1000} + . . . . + 10^{10000000000}) \div 7 \to (3^{10} + 3^{100} + 3^{1000} + . . . . . + 3^{10000000000}) \div 7 \to (3^{4} + 3^{4} + 3^{4} + 3^{4} + 3^{4} + 3^{4} + 3^{4} + 3^{4} + 3^{4} + 3^{4}) \div 7 = R e m a i n d e r o f 40 \div 7 \to 5.$

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