# Progression question

• Mar 2nd 2011, 07:11 AM
MichaelLight
Progression question
Find the value of the following series: i need help with (h). Thanks in advance... Attachment 21016
• Mar 2nd 2011, 07:44 AM
tonio
Quote:

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

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

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

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

Tonio
• Mar 2nd 2011, 09:11 AM
MichaelLight
Quote:

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

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

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

Tonio

Thanks for your reply. From the two formulas you provided above, only (1) looks familiar to me, as for the (2), is it possible for you to prove it (i.e. how to obtain that formula..)? Thanks....
• Mar 2nd 2011, 12:18 PM
tonio
Quote:

Originally Posted by MichaelLight
Thanks for your reply. From the two formulas you provided above, only (1) looks familiar to me, as for the (2), is it possible for you to prove it (i.e. how to obtain that formula..)? Thanks....

Google "geometric progression" or "geometric sequence"

Tonio
• Mar 3rd 2011, 03:03 AM
HallsofIvy
Or "geometric series".