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ISI B.Math Entrance Exam
2005 ISI B.Math Entrance Exam
2
B.Math - limit
B.Math - limit
Source:
June 20, 2012
limit
induction
calculus
calculus computations
Problem Statement
Let
a
1
=
1
a_1=1
a
1
=
1
and
a
n
=
n
(
a
n
−
1
+
1
)
a_n=n(a_{n-1}+1)
a
n
=
n
(
a
n
−
1
+
1
)
for all
n
≥
2
n\ge 2
n
≥
2
. Define :
P
n
=
(
1
+
1
a
1
)
.
.
.
(
1
+
1
a
n
)
P_n=\left(1+\frac{1}{a_1}\right)...\left(1+\frac{1}{a_n}\right)
P
n
=
(
1
+
a
1
1
)
...
(
1
+
a
n
1
)
Compute
lim
n
→
∞
P
n
\lim_{n\to \infty} P_n
lim
n
→
∞
P
n
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