[tex]S_n = \sum _{k = 1} ^{n} \frac{k}{2^k}[/tex]
Hva blir [tex]S_1[/tex], [tex]S_2[/tex] og [tex]S_3[/tex]?
Enkelt sum
Moderators: Vektormannen, espen180, Aleks855, Solar Plexsus, Gustav, Nebuchadnezzar, Janhaa
[tex]$${S_1} = \sum\limits_{k = 1}^1 {\frac{k}{{{2^k}}}} = \frac{1}{{{2^1}}}$$[/tex]
[tex]$${S_2} = \sum\limits_{k = 1}^2 {\frac{k}{{{2^k}}}} = \frac{1}{{{2^1}}} + \frac{2}{{{2^2}}}$$[/tex]
[tex]$${S_3} = \sum\limits_{k = 1}^3 {\frac{k}{{{2^k}}}} = \frac{1}{{{2^1}}} + \frac{2}{{{2^2}}} + \frac{3}{{{2^3}}}$$[/tex]
[tex]$${S_2} = \sum\limits_{k = 1}^2 {\frac{k}{{{2^k}}}} = \frac{1}{{{2^1}}} + \frac{2}{{{2^2}}}$$[/tex]
[tex]$${S_3} = \sum\limits_{k = 1}^3 {\frac{k}{{{2^k}}}} = \frac{1}{{{2^1}}} + \frac{2}{{{2^2}}} + \frac{3}{{{2^3}}}$$[/tex]
Takk 