MathDB
Problems
Contests
National and Regional Contests
Japan Contests
Today's Calculation Of Integral
2007 Today's Calculation Of Integral
176
176
Part of
2007 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 176
Source: Gunma University entrance exam 1969
2/4/2007
Let
f
n
(
x
)
=
∑
k
=
1
n
sin
k
x
k
(
k
+
1
)
.
f_{n}(x)=\sum_{k=1}^{n}\frac{\sin kx}{\sqrt{k(k+1)}}.
f
n
(
x
)
=
∑
k
=
1
n
k
(
k
+
1
)
s
i
n
k
x
.
Find
lim
n
→
∞
∫
0
2
π
{
f
n
(
x
)
}
2
d
x
.
\lim_{n\to\infty}\int_{0}^{2\pi}\{f_{n}(x)\}^{2}dx.
lim
n
→
∞
∫
0
2
π
{
f
n
(
x
)
}
2
d
x
.
calculus
integration
trigonometry
limit
induction
symmetry
calculus computations