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A sequence \((u_n)\) is defined for \(n \ge 0\) by the integral:$$ u_n = \int_0^1 x^n \,dx $$
Calculate the first three terms of the sequence: \(u_0\), \(u_1\), and \(u_2\).
Find a general formula for \(u_n\).
\(u_0=\)
\(\pi\)
\(e\)
\(x\)
\(n\)
\(u_n\)
\(f\)
\(i\)
\(\frac{a}{b}\)
\(\sqrt{\,}\)
\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
!
\(C\)
7
8
9
←
→
\(\sin{\,}\)
4
5
6
(
)
\(\cos{\,}\)
1
2
3
\(\times\)
\(\div\)
\(\tan{\,}\)
C
0
.
+
-
=
\(u_1=\)
\(\pi\)
\(e\)
\(x\)
\(n\)
\(u_n\)
\(f\)
\(i\)
\(\frac{a}{b}\)
\(\sqrt{\,}\)
\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
!
\(C\)
7
8
9
←
→
\(\sin{\,}\)
4
5
6
(
)
\(\cos{\,}\)
1
2
3
\(\times\)
\(\div\)
\(\tan{\,}\)
C
0
.
+
-
=
\(u_2=\)
\(\pi\)
\(e\)
\(x\)
\(n\)
\(u_n\)
\(f\)
\(i\)
\(\frac{a}{b}\)
\(\sqrt{\,}\)
\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
!
\(C\)
7
8
9
←
→
\(\sin{\,}\)
4
5
6
(
)
\(\cos{\,}\)
1
2
3
\(\times\)
\(\div\)
\(\tan{\,}\)
C
0
.
+
-
=
\(u_n=\)
\(\pi\)
\(e\)
\(x\)
\(n\)
\(u_n\)
\(f\)
\(i\)
\(\frac{a}{b}\)
\(\sqrt{\,}\)
\({a}^{b}\)
\(\ln{\,}\)
\(\log{\,}\)
!
\(C\)
7
8
9
←
→
\(\sin{\,}\)
4
5
6
(
)
\(\cos{\,}\)
1
2
3
\(\times\)
\(\div\)
\(\tan{\,}\)
C
0
.
+
-
=
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