Geometric Series please help!!
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Geometric Series please help!!

Geometric Series please help!!

[From: ] [author: ] [Date: 11-10-13] [Hit: ]
2^2 + 2^3 + 2^4 + ...2^3 + 2^4 + 2^5 + .........
Find Sn for a series with tn equal to each value:
d) 2^(n+1)

Can somebody help me out :S

-
t[1] + t[2] + t[3] + ... + t[x] =>
2^(1 + 1) + 2^(2 + 1) + 2^(3 + 1) + ... + 2^(x + 1)
2^2 + 2^3 + 2^4 + ... + 2^(x + 1) = S

Multiply everything by 2

2^3 + 2^4 + 2^5 + ... + 2^(x + 1) + 2^(x + 2) = 2S

2S - S = 2^(x + 2) - 2^2
S * (2 - 1) = 4 * 2^(x) - 4
S = 4 * (2^(x) - 1)

-
t_n = 2^(n + 1)

S_n = 2^2 (1 - 2^(n + 2))/(1 - 2) = 4 (2^(n + 2) - 1)
1
keywords: please,Series,help,Geometric,Geometric Series please help!!
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .