Number 111..............1 ( 91 times) is a

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8. Sequences and Series

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The number $111..............1$ ($91$ times) is a

A

Even number

B

Prime number

C

Not prime

D

None of these

Solution

(c) $S = 1 + 10 + {10^2} + …… + {10^{90}}$ ($91$ terms)

$ = \frac{{1.({{10}^{91}} – 1)}}{{10 – 1}} = \frac{{{{({{10}^{13}})}^7} – 1}}{{{{10}^{13}} – 1}} \times \frac{{{{10}^{13}} – 1}}{{10 – 1}}$

$ = [{({10^{13}})^6} + {({10^{13}})^5} + {({10^{13}})^4} + ……1]$

$({10^{12}} + {10^{11}} + …… + 1)$

It is the product of two integers and hence not prime.

Standard 11

Mathematics

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