PEEWSRIGWETRYqx

Answered

2022-01-01

To me the most common identity that comes to mind that results in 1 is the trigonometric sum of squared cosine and sine of an angle:

${\mathrm{cos}}^{2}\theta +{\mathrm{sin}}^{\theta}=1$ (1)

and maybe

$-{e}^{i\pi}=1$ (2)

Are there other famous (as in commonly used) identities that yield 1 in particular?

and maybe

Are there other famous (as in commonly used) identities that yield 1 in particular?

Answer & Explanation

jgardner33v4

Expert

2022-01-02Added 35 answers

Pick your favorite probability density function f, then

${\int}_{-\mathrm{\infty}}^{\mathrm{\infty}}f\left(x\right)dx=1$

Tiefdruckot

Expert

2022-01-03Added 46 answers

Vasquez

Expert

2022-01-08Added 457 answers

Here are two well-known infinite series whose sum is 1:

The following series is less known, interesting although:

where denominators form Sylvester sequence: every term is equal to the product of all previous terms, plus one. For example

2

3=2+1

7=2 * 3+1

43=2 * 3 * 7+1

1807=2 * 3 * 7 * 43+1

and so on

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