Search

Search results:

501.
Sum of the first n numbers
$1+2+3+ \cdots + n = \dfrac{n(n+1)}{2}$
Finite sum
502.
Sum of the first n even numbers
$2+4+6+ \cdots + 2n = n(n+1)$
Finite sum
503.
Sum of the first n odd numbers
$1+3+5+\ldots+(2n-1) = n^2$
Finite sum
504.
$k + (k+1) + \ldots + (k+n-1) = \dfrac{n(2k+n-1)}{2}$
Finite sum
505.
Sum of first n squares
$1^2+2^2+3^2+ \ldots + n^2 = \dfrac{n(n+1)(2n+1)}{6}$
Finite sum
506.
Sum of first n cubes
$1^3+2^3+3^3+ \ldots + n^3 = \left(\dfrac{n(n+1)}{2}\right)^2$
Finite sum
507.
Sum of first n odd squares
$1^2 + 3^2 + 5^2 + \ldots + (2n-1)^2 = \dfrac{n(4n^2-1)}{3}$
Finite sum
508.
Sum of first n odd cubes
$1^3+3^3+5^3+ \ldots + (2n-1)^3 = n^2(2n^2-1)$
Finite sum
509.
$\tan x = x + \dfrac{x^3}{3} + \dfrac{2x^5}{15} + \cdots + \dfrac{2^{2n}\left(2^{2n}-1\right)B_nx^{2n-1}}{(2n)!} \quad -\frac{\pi}{2} < x < \frac{\pi}{2}$
Power series
510.
$\dfrac{1}{1+x} = 1 - x + x^2 -x^3 + \cdots \quad -1 < x < 1$
Power series
511.
Circle perimeter
$P=2r\pi $
Circle
Perimeter
512.
Circle area
$A = r^2\pi$
Area
Circle
513.
Circle area - version 2
$A = \dfrac{\pi d^2}{4}$
514.
Circle area -verison 3
$ A = \dfrac{P \cdot r }{2}$
Area
Perimeter
515.
Circle arc - verison 1
$ s = r \cdot x $
Arc
Circle
516.
Circle arc
$ s = \dfrac{\pi r \alpha}{180\degree} $
Arc
Circle
517.
Sector area
$ B = \dfrac{r\cdot s}{2} $
Circle
Sector
518.
Sector area - version 2
$ B = \dfrac {r^2 \cdot x}{2} $
Circle
Sector
519.
Sector area - version 2
$ B = \dfrac{\pi \cdot r^2 \cdot \alpha}{360\degree} $
520.
Circle chord
$ a = 2\sqrt{2hr-h^2} $

© 2024 Milos Petrovic – All Rights Reserved