Find the remainder when
10 + 10² + 10³ + 10⁴ + ........ + 10⁹⁹ is divided by 6.

Answer:- 1

Explanation:-

Solution:

The remainder when 10 is divided by 6 is 4.
The remainder when 10² is divided by 6 is 4.
The remainder when 10³ is divided by 6 is 4.
The remainder when 10⁴ is divided by 6 is 4.
Thus, remainder is always 4.
So, the required remainder,

\begin{aligned} = \frac{4 + 4 + 4 + 4 + . . . . . 99 times}{6} \\ = \frac{396}{6} \end{aligned}

$\eqalign{ & = \frac{{4 + 4 + 4 + 4 + \,.....\,99{\text{ times}}}}{6} \cr & = \frac{{396}}{6} \cr}$
Thus, Required remainder is 0.

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Thus, Required remainder is 0. ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} = \frac{4 + 4 + 4 + 4 + . . . . . 99 times}{6} \\ = \frac{396}{6} \end{aligned}

$\eqalign{ & = \frac{{4 + 4 + 4 + 4 + \,.....\,99{\text{ times}}}}{6} \cr & = \frac{{396}}{6} \cr}$
Thus, Required remainder is 0. ", "dateCreated": "7/24/2019 10:09:12 AM" } }