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Sum of geometric series, from 1st to n th

ÀÛ¼ºÀÚ Uploader : prove ÀÛ¼ºÀÏ Upload Date: 2019-11-30º¯°æÀÏ Update Date: 2019-11-30Á¶È¸¼ö View : 317

In mathematics, a geometric series is a series with a constant ratio between successive terms.

a, ar, ar^2, ar^3, ¡¦, ar^(n-1)

S = a + ar + ar^2 + ar^3 + ¡¦ + ar^(n-1)

Sr = ar + ar^2 + ar^3 + ar^4 + ¡¦ + ar^n

S-Sr = a - ar^n = a(1-r^n)

S(1-r) = a(1-r^n)

S = a(1-r^n)/(1-r), r ¡Á 1

if r < 1 and n¡æ¡Ä then r^n=0, therefore S = a/(1-r)

*** Âü°í¹®Çå[References] ***

https://en.wikipedia.org/wiki/Geometric_series
S = a*(1-r^n)/(1-r)
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