Sumatorias Importantes - U

Sumatorias Importantes
Profesor: Jorge San Martín
Auxiliares: Francisco Jiménez - Ramiro Villagra
n
X
i
=
n(n + 1)
2
i2
=
i3
=
n(n + 1)(2n + 1)
6
2
n(n + 1)
2
i4
=
n(n + 1)(2n + 1)(3n2 + 3n − 1)
30
r
=
nr
ri
=
1 − rn+1
1−r
ri
=
rn+1 − r
r−1
=
rn − 1
rn+1 − an
=
1−
=
(n + 1)! − 1
i=1
n
X
i=1
n
X
i=1
n
X
i=1
n
X
i=1
n
X
i=0
n
X
i=1
n
X
1
i
r
i=1
n
X
1
i(i + 1)
i=1
n
X
i · i!
1
n+1
i=0
1