### Related

##### simpsum-sum-sumexpand

sum((w^i)*i, i, 0, n)...

sum(w**i,i,0,n),simpsum;

Calculate

##### simpsum-sum

p: ((1-x^6)/(1-x))^5;

c(x, y):= x!/(y!*(x-y...

d(a, b, o, t):= sum((...

Calculate

##### simpsum-sum

sum(2*k+1,k,1,n),simp...

Calculate

##### simpsum-sum

sum(n,n,inf,1), simpsum;

Calculate

##### simpsum-sum

sum(2*k-1,k,1,n);

f(k):=sum(2*k-1,k,1,n...

Calculate

##### simpsum-sum

sum(n^1,n,inf,1), sim...

Calculate

##### simpsum

simpsum:truesum( (n-i...

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##### simpsum-sum

sum( sum(c**i, i, 0, ...

Calculate

##### simpsum

F(n):=2^(2^n)+1, simp...

F(3);

Calculate

##### simpsum-sqrt-sum

sum ((s^2-r^2-(-2*i*s...

s=4;

Calculate

### simpsum

Run Example
```(%i1)sum((-1^n)/(2^n), n, 0, inf), simpsum;
(%o1)                                 - 2
(%i2) ```
Run Example
```a(n):=product(n+k,k,0,10)/11!;
product(n + k, k, 0, 10)
(%o1)                  a(n) := ------------------------
11!
(%i2) simpsum:true;
(%o2)                                true
(%i3) s(n):=sum(a(k),k,1,n);
(%o3)                     s(n) := sum(a(k), k, 1, n)
(%i4) factor(s(n));
(%o4) (n (n + 1) (n + 2) (n + 3) (n + 4) (n + 5) (n + 6) (n + 7) (n + 8)
(n + 9) (n + 10) (n + 11))/479001600
(%i5) g(n):=12^(1/3)*(23100*(s(n)+10))^(1/12)-11/2;
1/3                    1/12   11
(%o5)             g(n) := 12    (23100 (s(n) + 10))     - --
2
(%i6) expand(g(n));
12         11       10         9
1/6  1/6   1/3    1/12         n          n        n       11 n
(%o6) 2    5    12    231     expt(--------- + ------- + ------ + ------
479001600   7257600   248832   161280
8         7           6           5           4           3
10831 n    1903 n    242537 n    139381 n    341747 n    190553 n
+ -------- + ------- + --------- + --------- + --------- + ---------
14515200   345600     8709120     1451520     1555200     604800
2
83711 n    n        1     11
+ -------- + -- + 10, --) - --
332640    12       12    2
(%i7) h(n):=n-g(n);
(%o7)                          h(n) := n - g(n)
(%i8) diff(h(n),n);
11        10        9        7        5        3
24 n   + 132 n   + 220 n  - 264 n  + 264 n  - 132 n  + 20 n
(%o8) 1 - (-----------------------------------------------------------
24
10         9         8         6         4        2
330 n   + 1650 n  + 2475 n  - 2310 n  + 1650 n  - 495 n  + 25         9
+ ------------------------------------------------------------- + 1320 n
6
8           7           6           4          2
54450 n  + 217800 n  + 254100 n  - 127050 n  + 36300 n  - 1815         8
+ -------------------------------------------------------------- + 5940 n
3
7            6            5            3
1262184 n  + 4417644 n  + 4417644 n  - 1472548 n  + 210364 n         7
+ ------------------------------------------------------------ + 7920 n
8
6            5            4           2
1804110 n  + 5412330 n  + 4510275 n  - 902055 n  + 42955
+ --------------------------------------------------------
2
5             4             3
20501580 n  + 51253950 n  + 34169300 n  - 3416930 n         5
+ --------------------------------------------------- - 5544 n
6
4             3             2
25228500 n  + 50457000 n  + 25228500 n  - 840950             3             2
+ ------------------------------------------------ + 12756216 n  + 29759004 n
3
12       11       10       8       6       4       2       11        10        9        7        5        3                          9          8          7          5          3                             8           7           6           4           2                    7           6           5           3                      6             5            4            2                     5             4            3
11/6  11/6   11/3    11/12       2 n   + 12 n   + 22 n   - 33 n  + 44 n  - 33 n  + 10 n    30 n   + 165 n   + 275 n  - 330 n  + 330 n  - 165 n  + 25 n        10   6050 n  + 27225 n  + 36300 n  - 25410 n  + 12100 n  - 1815 n        9   157773 n  + 631092 n  + 736274 n  - 368137 n  + 105182 n         8   257730 n  + 902055 n  + 902055 n  - 300685 n  + 42955 n   3416930 n  + 10250790 n  + 8542325 n  - 1708465 n         6   5045700 n  + 12614250 n  + 8409500 n  - 840950 n            4            3             2
+ 20633832 n + 3585840)/(2     5     12     231      expt((------------------------------------------------------- + ----------------------------------------------------------- + 132 n   + ------------------------------------------------------------ + 660 n  + --------------------------------------------------------- + 990 n  + ------------------------------------------------------- + -------------------------------------------------- - 924 n  + ------------------------------------------------ + 3189054 n  + 9919668 n  + 10316916 n  + 3585840 n)/39916800 + 10,
24                                                           6                                                                       3                                                                      8                                                                   2                                                      6                                                            3
11
--))
12
(%i9) factor(479001600);
10  5  2
(%o9)                           2   3  5  7 11
(%i10) factor(11!);
8  4  2
(%o10)                           2  3  5  7 11
(%i11) ```
Run Example
```f:1/(1+x);
1
(%o1)                                -----
x + 1
(%i2) s(n,x):=integrate((-x)^n,x,0,1);
n
(%o2)                s(n, x) := integrate((- x) , x, 0, 1)
(%i3) s(0,x);
(%o3)                                  1
(%i4) s(1,x);
1
(%o4)                                 - -
2
(%i5) s(2,x);
1
(%o5)                                  -
3
(%i6) s(3,x);
1
(%o6)                                 - -
4
(%i7) g3:sum((-x)^k,k,0,3);
3    2
(%o7)                          - x  + x  - x + 1
(%i8) g:sum((-x)^k,k,0,n-1),simpsum;
n
(- x)  - 1
(%o8)                             ----------
- x - 1
(%i9) S3:integrate(g3,x,0,1);
7
(%o9)                                 --
12
(%i10) fmg:f-g;
n
1     (- x)  - 1
(%o10)                        ----- - ----------
x + 1    - x - 1
(%i11) fmg:factor(fmg);
n
(- x)
(%o11)                              ------
x + 1
(%i12) ```

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