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Today's Calculation Of Integral
2006 Today's Calculation Of Integral
164
164
Part of
2006 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 164
Source: Nara Women's University　entrance exam/Science
10/21/2006
For positive integers
n
,
n,
n
,
let
S
n
=
1
1
+
1
2
+
⋯
⋯
+
1
n
,
T
n
=
1
1
+
1
2
+
1
2
+
1
2
+
⋯
⋯
+
1
n
+
1
2
.
S_{n}=\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\cdots\cdots+\frac{1}{\sqrt{n}},\ T_{n}=\frac{1}{\sqrt{1+\frac{1}{2}}}+\frac{1}{\sqrt{2+\frac{1}{2}}}+\cdots\cdots+\frac{1}{\sqrt{n+\frac{1}{2}}}.
S
n
=
1
1
+
2
1
+
⋯⋯
+
n
1
,
T
n
=
1
+
2
1
1
+
2
+
2
1
1
+
⋯⋯
+
n
+
2
1
1
.
Find
lim
n
→
∞
T
n
S
n
.
\lim_{n\to\infty}\frac{T_{n}}{S_{n}}.
lim
n
→
∞
S
n
T
n
.
calculus
integration
limit
calculus computations