A) Even number
B) Prime number
C) Not prime
D) None of these
Correct Answer: C
Solution :
\[S=1+10+{{10}^{2}}+......+{{10}^{90}}\] (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.
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