Summing expanding cells without helper column

[ttombozara]

Please help.<o></o>

<o> </o>	A<o></o>​	B<o></o>​	C<o></o>​	D<o></o>​
1<o></o>​	20<o></o>​	20<o></o>​	<o> </o>​	20<o></o>​
2<o></o>​	18<o></o>​	38<o></o>​	<o> </o>​	0.9<o></o>​
3<o></o>​	16.2<o></o>​	54.2<o></o>​	<o> </o>​	<o> </o>​
4<o></o>​	14.58<o></o>​	68.78<o></o>​	<o> </o>​	<o> </o>​
5<o></o>​	13.122<o></o>​	81.902<o></o>​	<o> </o>​	<o> </o>​
6<o></o>​	11.8098<o></o>​	93.7118<o></o>​	<o> </o>​	<o> </o>​
7<o></o>​	10.62882<o></o>​	104.3406<o></o>​	<o> </o>​	<o> </o>​

<tbody> </tbody>

<o></o>
Formula in cell A1: =$D$1*$D$2^(ROWS($A$1:A1)-ROWS($A$1))<o></o>
Formula in cell A1: =SUM($A$1:A1)<o></o>
I would like to get rid of column A, helper column, and pu**** formula into an array to straight away compute the results in column B.<o></o>
Thank in advance for your help.

Tom
PS: Apology for the layout of my data which may not comply withthe norm of this forum.

 

[Peter_SSs]

If you are happy to have the results start in row 2 instead of row 1, here is one way.
Formula in B2 is copied down.

Excel 2016 (Windows) 32 bit
	B	C	D
1	Direct		20
2	20		0.9
3	38
4	54.2
5	68.78
6	81.902
7	93.7118
8	104.34062
Without Helper

Cell Formulas
Range	Formula
B2	=SUM(B1,D$1*D$2^(ROWS(B$2:B2)-1))

 

[Marcelo Branco]

Or using the formula that calculates the sum of the terms of a geometric progression
S = a1 * (q^n-1)/(q-1)
maybe this...

	A​	B​	C​	D​
1​		20​		20​
2​		38​		0,9​
3​		54,2​
4​		68,78​
5​		81,902​
6​		93,7118​
7​		104,3406​

Formula in B1 copied down
=D$1*(D$2^ROWS(B$1:B1)-1)/(D$2-1)

M.

 

[ttombozara]

Great!!!!!!!!!!!!!
Many thanks, you great people for your help. It did work perfectly. With many heads together, things can easily be solved.
* Peter_SSs: starting in row 2 is not a major problem, thank you;
* Marcelo Branco: what can I say. I am supposed to be a maths teacher, I completely forgot it although I am solving a problem of a geometric progression. Many thanks.

Maybe see you again sometimes.

Tom

 

[Aladin Akyurek]

[...]
* Marcelo Branco: what can I say. I am supposed to be a maths teacher, I completely forgot it although I am solving a problem of a geometric progression. [...]

It must be rather due to the interference from the solution in Excel that you embarked upon.

 

[Marcelo Branco]

* Marcelo Branco: what can I say. I am supposed to be a maths teacher, I completely forgot it although I am solving a problem of a geometric progression. Many thanks.

Tom
You are welcome. Thanks for the feedback.
I must confess that i also took time to identify that it was a mere problem of geometric progression.
I tried to use Excel functions, etc, etc, until ... it came! And then i remembered (deduced). the formula

M.