Binomial Theorem And Its Simple Applications Question 177
Question: The number 111……1 (91 times) is
[UPSEAT 1999]
Options:
A) Not a prime
B) An even number
C) Not an odd number
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- 111…………..1 (91 times) = $ 1+10+10^{2}+…..+10^{90} $ = $ \frac{10^{91}-1}{10-1}=\frac{{{(10^{7})}^{13}}-1}{10-1} $ = $ \frac{t^{13}-1}{9} $ ,
where $ t=10^{7} $ = $ ( \frac{t-1}{9} ),(t^{12}+t^{11}+…..+t+1) $ = $ ( \frac{10^{7}-1}{10-1} ),(1+t+t^{2}+….+t^{12}) $
$ =(1+10+10^{2}+….+10^{6})(1+t+t^{2}+…+t^{12}) $ \ $ 111…..1(91\text{times)} $ is a composite number.
BETA
