four arguments
an expression, the name of the variable (for
example n), and the bounds (for example a and b).
sum returns the discrete sum of this expression with respect to
the variable from a to b.
Input :
sum(1,k,-2,n)
Output :
n+1+2
Input :
normal(sum(2*k-1,k,1,n))
Output :
n^
2
Input :
sum(1/(n^
2),n,1,10)
Output :
1968329/1270080
Input :
sum(1/(n^
2),n,1,+(infinity))
Output :
pi^
2/6
Input :
sum(1/(n^
3-n),n,2,10)
Output :
27/110
Input :
sum(1/(n^
3-n),n,1,+(infinity))
Output :
1/4
This result comes from the decomposition of
.
Input :
partfrac(1/(n^
3-n))
Output :
1/(2*(n+1))-1/n+1/(2*(n-1))
Hence :
-
= - 
= -
- 
-
*
=
*(
) =
*(1 +
+ 
)
*
=
*(
+
+
)
After simplification by
, it remains :
-
+
*(1 +
) -
+
*(
+
) =
-
Therefore :
- for N = 10 the sum is equal to :
1/4 - 1/220 = 27/110
- for N = +
the sum is equal to : 1/4 because
approaches zero when N approaches infinity.