What is the remainder when 7 7 + 7 77 + 7 777 + 7 7777 . . . . . . . . . + 7 77777777 is divided by 8? Options: A . &nbsp-1 B . &nbsp1 C . &nbsp7 D . &nbsp0 E . &nbspCannot be determined

Answer: Option D : D 7 8 remainder = -1 Thus, any odd power of 7, when divided by 8, will give a remainder of -1 itself. ( − 1 ) 7 + ( − 1 ) 77 + ( − 1 ) 777 . . . . . . 8 = -1-1-1-...8 times = - 8 The remainder when -8 is divided by 8, is 0.

What is the remainder when 77+777+7777+77777.........+777777777 is divided by 8?

Question

What is the remainder when

7^{7} + 7^{77} + 7^{777} + 7^{7777} . . . . . . . . . + 7^{77777777}

is divided by 8?

Answer: Option D
:
D

\frac{7}{8}

remainder = -1
Thus, any odd power of 7, when divided by 8, will give a remainder of -1 itself.

\frac{(- 1)^{7} + (- 1)^{77} + (- 1)^{777} . . . . . .}{8}

= -1-1-1-...8 times = - 8
The remainder when -8 is divided by 8, is 0.

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