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ISI Entrance Examination
2020 ISI Entrance Examination
4
4
Part of
2020 ISI Entrance Examination
Problems
(1)
ISI 2020 : Problem 4
Source: B.Stat & B.Math Entrance Exam 2020
9/20/2020
Let a real-valued sequence
{
x
n
}
n
⩾
1
\{x_n\}_{n\geqslant 1}
{
x
n
}
n
⩾
1
be such that
lim
n
→
∞
n
x
n
=
0
\lim_{n\to\infty}nx_n=0
n
→
∞
lim
n
x
n
=
0
Find all possible real values of
t
t
t
such that
lim
n
→
∞
x
n
(
log
n
)
t
=
0
\lim_{n\to\infty}x_n\big(\log n\big)^t=0
lim
n
→
∞
x
n
(
lo
g
n
)
t
=
0
.
isi
2020
real analysis