We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
1
203
4
avatar

\(\[1 \cdot \frac {1}{2} + 2 \cdot \frac {1}{4} + 3 \cdot \frac {1}{8} + \dots + n \cdot \frac {1}{2^n} + \dotsb.\]\)Compute 

 Nov 8, 2018
 #1
avatar+5652 
+1

it's so urgent you couldn't post the image so we could see it!

 Nov 8, 2018
 #2
avatar
+1

\(\[1 \cdot \frac {1}{2} + 2 \cdot \frac {1}{4} + 3 \cdot \frac {1}{8} + \dots + n \cdot \frac {1}{2^n} + \dotsb.\]\)

.
 Nov 8, 2018
 #3
avatar
+1

∑[n/(2^n), n, 1, ∞] =2

Here is the partial sum formula:

sum_(n=1 to m) = n/2^n = 2^(-m) (-m + 2^(m + 1) - 2)

 Nov 8, 2018
edited by Guest  Nov 8, 2018
 #4
avatar+4299 
+1

Here, we can use \(\frac{n}{1-r}\)  , so  \(\frac{1}{1-\frac{1}{2}}=\frac{1}{\frac{1}{2}}=\boxed{2}\) .

 Nov 9, 2018

19 Online Users