Sorry that I don't know the correct notation. I'll try to explain with my own words.
In this case n is not a variable in the way that you can choose what number is n. You simply have to calculate the function for every possible number n from 1 to ∞ and then take the sum of all those solutions.
Let's first take the function: f1(x)=x *10^-n or f1(x)=xE(-n)
n is not a variable, let's say it's a constant, by example 2
then for x=3,x=6 or x=9; f1(x)=0.03, f1(x)=0.06 or f1(x)=0.09
Now we make a new function: f2(x) is the sum of all possible solutions of f1(x) for n=1 to n=4 (if I'm right, for that sum thing the Σ sign is used)
then for x=3, 6 or 9; f2(x)=0.3333, 0.6666 or 0.9999
But in this case it's not about n=1 to 4, but it should be n=1 to ∞ (I think then it's called a limit, for it goes to ∞)
Then we have a function f3(x), what's the sum of all possible solutions of f1(x) for n=1 to ∞
Then for:
x=3; f3(x)=0.33333333333......=1/3
x=6; f3(x)=0.66666666666......=2/3
x=9; f3(x)=0.99999999999......=3/3=1
So, the variable of the function is not n but it's x, and in the case of your "mathematical problem" the variable x is 9.
And again, I don't know the correct notations and terms, so I don't know how I have to call n in this case, but it's definitaly not just a variable.
We can also make a computerprogram to calculate this. And again, I'll probably make mistakes with the right notations, but I hope you'll understand what I mean.
Code: Select all
input or get x 'ask user to enter x (=9)
n=1
f3=0
do
f1=x*10^-n
f3=f3+f1
n=n+1
loop until n=∞
print or write f3 'put the answer on the screen
Now I can tell you a few things
1, The computer will not be able to calculate this, for it doesn't know what ∞ means.
2, If the computer would know what that means, it would be working until eternity. (probably it would say: Memory acces violation
)
3, If the computer was able to finish this program, it would say: 1
