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8. Sequences and Series
medium
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