Find the value of the following series: i need help with (h). Thanks in advance... Attachment 21016

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- Mar 2nd 2011, 06:11 AMMichaelLightProgression question
Find the value of the following series: i need help with (h). Thanks in advance... Attachment 21016

- Mar 2nd 2011, 06:44 AMtonio

$\displaystyle \displaystyle{\sum\limits^{10}_{r=1}\left(4r+\left (\frac{16}{5}\right)^r\right)=4\sum\limits^{10}_{r =1}r+\sum\limits^{10}_{r=1}\left(\frac{16}{5}\righ t)^r$ , and now the hints:

1) For any $\displaystyle \displaystyle{n\in\mathbb{N}\,,\,\,\sum\limits^n_{ k=1}k=\frac{n(n+1)}{2}}$ ;

2) for any $\displaystyle \displaystyle{1\neq a\in\mathbb{R}\,,\,n\in\mathbb{N}\,,\,\,\sum\limit s^n_{k=1}a^k=\frac{a^{n+1}-1}{a-1}}$

Now solve your problem (h)...(Wink)

Tonio - Mar 2nd 2011, 08:11 AMMichaelLight
- Mar 2nd 2011, 11:18 AMtonio
- Mar 3rd 2011, 02:03 AMHallsofIvy
Or "geometric

**series**".