mariamikayla
Answered

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Please, solve this exercice:

1+2+2²+2³+2⁴+....+ 2²⁰¹¹

It can be solved by using geometric progression?

Sagot :

[tex]1+2+2^2+2^3+2^4+...+2^{2011}\\\\a_1=1;\ a_2=1\cdot2=2;\ a_3=2\cdot2=2^2;\ a_4=2^2\cdot2=2^3\\\vdots\\a_{2012}=2^{2010}\cdot2=2^{2011}[/tex]

[tex]The\ sum\ of\ a\ terms\ of\ geometric\ progression:S_n=\frac{a_1(1-r^n)}{1-r}\\\\a_1=1;\ r=2\\\\subtitute:\\\\S_{2012}=\frac{1(1-2^{2012})}{1-2}=\frac{1-2^{2012}}{-1}=2^{2012}-1\\\\Only\ that...(606\ digits,\ if\ you\ want\ how\ length\ this\ number)[/tex]
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