Syntax for a series summation (Sigma)

[upshaw211]

I need to find out how to input a series summation in Excel, similar t
Sigma notation.

The formula I need to input is [(x*C)^i]/factorial(i) From (i=0) t
(i=x-1) and where C is a constant.

The length of the series depends on the value of x, but x is a variabl
which can be assigned different values, so I cannot simply write out th
whole formula based on a certain value of x.

Any help will be GREATLY appreciated. Thanks

 

[duane]

two ways to do it - first would be a macro - fairly simple. here i
another way

x in cell b3
C in cell b4
i values in column 0 in a8
=IF(A8+1<$B$3,A8+1,0) in a9
=IF(A9=0,0,IF(A9+1<$B$3,A9+1,0)) in a10 to as far as you need to excee
x rows

in cell b8
=$B$3*$B$4^A8/FACT(A8)
in cell b9 to as far as you put in eqs in column a
=IF(A9=0,0,$B$3*$B$4^A9/FACT(A9))

in cell c8 and as far as eqs in column a and b
=SUM($B$8:B8)

the result will be the max of column

 

[duane]

need some parenthesis

in cell b8
=($B$3*$B$4)^A8/FACT(A8)
in cell b9 to as far as you put in eqs in column a
=IF(A9=0,0,($B$3*$B$4)^A9/FACT(A9)

 

[Dana DeLouis]

If "x" is an integer, would this work? Here, I use two range names (x, c_)

= (EXP(c_ * x) * EXP(GAMMALN(x)) * (1 - GAMMADIST(c_ * x, x, 1, TRUE))) /
FACT(x - 1)

May not be the best idea, but it may work for your situation.

HTH

 

[AlfD]

Hi!

Maybe back to first principles.

The sequence you are summing looks like the sum of Ui from i= 0 to i
x-1 where Ui+1 = Ui*C*x/(i+1).

U0 by convention is 1.

Put 1 in A1

Put a value for C in A7 and a value for x in A8 (arbitrarily chosen).

Put =A1*$A$7*$A$8/(COLUMN()-1) in B1.

Copy this across as far as you like (which is at least as far as
columns)
I appreciate x is not fixed, but convergence will suggest a suitabl
maximum number of terms for the series. Trial and error...

Now put in A2 = sum (A1:M1) (or more than M if you are going to suc
lengths).

Al

 

[AlfD]

PS:

x=0.5 and C=2 gives a passable value for- e- very quickly.

Al

 

[Dana DeLouis]

Oops. Didn't see this. For an approximation, if I use 'k' instead of C,
and keep k relatively small, then a slightly shorter version might be

=(EXP(k*x)*(1-GAMMADIST(k*x,x,1,TRUE)))

Using Myrna's excellent idea for a reference with k=3, and x=10, I get
76,106,409.66

This is close to Myrna's more exact value of
76,106,409.57

I would use Myrna's excellent idea as this is only an approximate value as
long as k is relatively small. (Microsoft did not update some important
functions still in Excel 2003) :>(

Anyway, HTH.
--
Dana DeLouis
Win XP & Office 2003

If "x" is an integer, would this work? Here, I use two range names (x,
c_)

= (EXP(c_ * x) * EXP(GAMMALN(x)) * (1 - GAMMADIST(c_ * x, x, 1, TRUE))) /
FACT(x - 1)

May not be the best idea, but it may work for your situation.

HTH
--
Dana DeLouis
Win XP & Office 2003

I need to find out how to input a series summation in Excel, similar to
Sigma notation.

The formula I need to input is [(x*C)^i]/factorial(i) From (i=0) to
(i=x-1) and where C is a constant.

The length of the series depends on the value of x, but x is a variable
which can be assigned different values, so I cannot simply write out the
whole formula based on a certain value of x.

Any help will be GREATLY appreciated. Thanks.

 

[AlfD]

Hi!

It would be good to know from the OP whether s/he is interested i
convergent or divergent series. Maybe even a preferred range for x an
C.

Al

 

[Myrna Larson]

Hi, Dana:

I don't know if he'll ever see the array formulas. I posted these in response
to his duplicate post in worksheet.functions....

Myrna Larson