isi-entrance 2015 Q24

isi-entrance · India · UGB 4 marks Sequences and series, recurrence and convergence Multiple-choice on sequence properties
For any integer $n \geq 1$, define $a _ { n } = \frac { 1000 ^ { n } } { n ! }$. Then the sequence $\left\{ a _ { n } \right\}$
(a) does not have a maximum
(b) attains maximum at exactly one value of $n$
(c) attains maximum at exactly two values of $n$
(d) attains maximum for infinitely many values of $n$.
(c) Find out the first values of $n$ for which $\frac { a _ { n + 1 } } { a _ { n } }$ becomes $< 1$. 
For any integer $n \geq 1$, define $a _ { n } = \frac { 1000 ^ { n } } { n ! }$. Then the sequence $\left\{ a _ { n } \right\}$\\
(a) does not have a maximum\\
(b) attains maximum at exactly one value of $n$\\
(c) attains maximum at exactly two values of $n$\\
(d) attains maximum for infinitely many values of $n$.
Paper Questions
QB1 QB10 QB11 QB2 QB3 QB4 QB5 QB6 QB7 QB8 QB9 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28