Logan Wyatt

2022-07-10

How to divide the fraction $1/1+1$

This has to do with re-calculating the sigmoid function in ai. It isn't really important, but the simplest way to put it is I need a math guru to help my monkey brain do this:

$\frac{1}{1+e}$

to like

$\frac{1}{something}+\frac{1}{e}$

Please help me remember my math from high-school if this was ever taught to us.

This has to do with re-calculating the sigmoid function in ai. It isn't really important, but the simplest way to put it is I need a math guru to help my monkey brain do this:

$\frac{1}{1+e}$

to like

$\frac{1}{something}+\frac{1}{e}$

Please help me remember my math from high-school if this was ever taught to us.

Allison Pena

Beginner2022-07-11Added 14 answers

The problem is that there isn't really a good way to do that. Things that do work with fractions are the following:

1.$\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$

2.$\frac{a\cdot b}{c\cdot d}=\frac{a}{c}\cdot \frac{b}{d}$

but there isn't a way to separate when there is a sum in the denominator.

I suppose perhaps one thing you could do, although this isn't likely what you have in mind, is the following: if $e$ is small in your description (that is, if $|e|<1$) then there is a geometric series expansion

$\frac{1}{1+e}=1-e+{e}^{2}-{e}^{3}+{e}^{4}+\cdots =\sum _{n=0}^{\mathrm{\infty}}(-1{)}^{n}{e}^{n}$

but I'm not so certain this is what you're looking for.

1.$\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$

2.$\frac{a\cdot b}{c\cdot d}=\frac{a}{c}\cdot \frac{b}{d}$

but there isn't a way to separate when there is a sum in the denominator.

I suppose perhaps one thing you could do, although this isn't likely what you have in mind, is the following: if $e$ is small in your description (that is, if $|e|<1$) then there is a geometric series expansion

$\frac{1}{1+e}=1-e+{e}^{2}-{e}^{3}+{e}^{4}+\cdots =\sum _{n=0}^{\mathrm{\infty}}(-1{)}^{n}{e}^{n}$

but I'm not so certain this is what you're looking for.

Patatiniuh

Beginner2022-07-12Added 5 answers

I suppose that the question is less elementary than only finding $\frac{1}{1+e}=\frac{1}{e}-\frac{1}{e(1+e)}$

May be you want to express $\frac{1}{1+e}$ in terms of $\frac{1}{e}$?

If so, use a geometric series :

$\frac{1}{1+e}=\frac{\frac{1}{e}}{1+\frac{1}{e}}=\frac{1}{e}-{\left(\frac{1}{e}\right)}^{2}+{\left(\frac{1}{e}\right)}^{3}-{\left(\frac{1}{e}\right)}^{4}+...$

$\frac{1}{1+e}=-\sum _{n=1}^{\mathrm{\infty}}{(-\frac{1}{e})}^{n}$

May be you want to express $\frac{1}{1+e}$ in terms of $\frac{1}{e}$?

If so, use a geometric series :

$\frac{1}{1+e}=\frac{\frac{1}{e}}{1+\frac{1}{e}}=\frac{1}{e}-{\left(\frac{1}{e}\right)}^{2}+{\left(\frac{1}{e}\right)}^{3}-{\left(\frac{1}{e}\right)}^{4}+...$

$\frac{1}{1+e}=-\sum _{n=1}^{\mathrm{\infty}}{(-\frac{1}{e})}^{n}$

Which expression has both 8 and n as factors???

One number is 2 more than 3 times another. Their sum is 22. Find the numbers

8, 14

5, 17

2, 20

4, 18

10, 12Perform the indicated operation and simplify the result. Leave your answer in factored form

$\left[\frac{(4x-8)}{(-3x)}\right].\left[\frac{12}{(12-6x)}\right]$ An ordered pair set is referred to as a ___?

Please, can u convert 3.16 (6 repeating) to fraction.

Write an algebraic expression for the statement '6 less than the quotient of x divided by 3 equals 2'.

A) $6-\frac{x}{3}=2$

B) $\frac{x}{3}-6=2$

C) 3x−6=2

D) $\frac{3}{x}-6=2$Find: $2.48\xf74$.

Multiplication $999\times 999$ equals.

Solve: (128÷32)÷(−4)=

A) -1

B) 2

C) -4

D) -3What is $0.78888.....$ converted into a fraction? $\left(0.7\overline{8}\right)$

The mixed fraction representation of 7/3 is...

How to write the algebraic expression given: the quotient of 5 plus d and 12 minus w?

Express 200+30+5+4100+71000 as a decimal number and find its hundredths digit.

A)235.47,7

B)235.047,4

C)235.47,4

D)234.057,7Find four equivalent fractions of the given fraction:$\frac{6}{12}$

How to find the greatest common factor of $80{x}^{3},30y{x}^{2}$?