u n = a r n − 1 s n = a ( r n − 1 ) r − 1 bila r > 1 s n = a ( 1 − r n ) 1 − r bila r < 1 r = u n u n − 1 u t = u 1 u n r = a n a k n − k nb: n dan k adalah suku ke-n dan suku ke-k. {\displaystyle {\begin{aligned}u_{n}&=ar^{n-1}\\s_{n}&={\frac {a(r^{n}-1)}{r-1}}{\text{bila}}r>1\\s_{n}&={\frac {a(1-r^{n})}{1-r}}{\text{bila}}r<1\\r&={\frac {u_{n}}{u_{n-1}}}\\u_{t}&={\sqrt {u_{1}u_{n}}}\\r&={\sqrt[{n-k}]{\frac {a_{n}}{a_{k}}}}\\{\text{nb: n dan k adalah suku ke-n dan suku ke-k.}}\\\end{aligned}}}
S t u r u n = a 1 − r S n a i k = a r 1 − r S t o t a l = a 1 − r + a r 1 − r = a + a r 1 − r = 2 a − a + a r 1 − r = 2 a − ( a − a r ) 1 − r = 2 a 1 − r − a − a r 1 − r = 2 a 1 − r − a ( 1 − r ) 1 − r = 2 S ∞ − a {\displaystyle {\begin{aligned}S_{turun}&={\frac {a}{1-r}}\\S_{naik}&={\frac {ar}{1-r}}\\S_{total}&={\frac {a}{1-r}}+{\frac {ar}{1-r}}\\&={\frac {a+ar}{1-r}}\\&={\frac {2a-a+ar}{1-r}}\\&={\frac {2a-(a-ar)}{1-r}}\\&={\frac {2a}{1-r}}-{\frac {a-ar}{1-r}}\\&={\frac {2a}{1-r}}-{\frac {a(1-r)}{1-r}}\\&=2S_{\infty }-a\\\end{aligned}}}
![{\displaystyle {\begin{aligned}u_{n}&=ar^{n-1}\\s_{n}&={\frac {a(r^{n}-1)}{r-1}}{\text{bila}}r>1\\s_{n}&={\frac {a(1-r^{n})}{1-r}}{\text{bila}}r<1\\r&={\frac {u_{n}}{u_{n-1}}}\\u_{t}&={\sqrt {u_{1}u_{n}}}\\r&={\sqrt[{n-k}]{\frac {a_{n}}{a_{k}}}}\\{\text{nb: n dan k adalah suku ke-n dan suku ke-k.}}\\\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ea88d5735ded2d65879e8e8d2c45a9de41869309)
![{\displaystyle R={\sqrt[{n}]{a_{1}\cdot a_{2}\cdot a_{3}\cdot \dots \cdot a_{n}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ffc4da1935dfe1b5e695f650d779e91e8747b53f)
![{\displaystyle r_{b}={\sqrt[{x+1}]{r}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a40486aa76cc83db94a68e91fc855fe239ac1c42)
