# Math Help - Progression question

1. ## Progression question

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

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

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

3. 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....

4. 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

5. Or "geometric series".