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Question

The value of 413.419.4127.......... is


A

2

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B

3

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C

4

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D

9

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Solution

The correct option is A

2


Explanation for the correct answer:

By using the properties of indices we can write

413.419.4127..........=413+19+127+......

The exponent is the sum of an infinite geometric progression with the first term as 13 and common ratio as 13

The sum of an infinite geometric progression is given as

S=a1-r

We have , a=r=13

S=131-13

=1323

S=12

413.419.4127..........=412

413.419.4127..........=2

Hence, the value of 413.419.4127.......... is 2.

Hence, option A is the correct answer.


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