Question 41545
1 + 1/2 + 1/3 + 1/4 + 1/9 + 1/8 + 1/27 + 1/16 + ...

excuse me as you'll have to post 
<h6><pre>"Find the sum of the following series: 

1 + 1/2 + 1/3 + 1/4 + 1/9 + 1/8 + 1/27 + 1/16 + ...


I tried to use the sume of an infinite series formula, but there is no common<br> ratio. I also tried seeing if some of the terms will cancel or add<br> up to the same thing, but I am still not getting anywhere."</pre></h6>
again, but do the numbers have a pattern at all? <br>1+1/2+1/3+1/4+<b>1/9</b>+1/8+<b>1/27</b>+<i>1/16</i>...?
Do you mean 1+1/2+1/3...?
<hr>
Hey I found it!
it's 1/1+1/2+1/3+1/4+1/9+1/8
you see, 4 is 2*2, 8 is 4*2, 9 is 3*3, get it?
it's the sum of two infinite series:
1/3+1/9+1/27 etc..
AND 1/1+1/2+1/4+1/8...
<font color=yellow>1/1+</font><font color=green>1/2+<font color=red>1/3+</font>1/4+<font color=red>1/9+</font>1/8+<font color=red>1/27+</font>1/16...</font>
COOL!  so now just use the formula (which I can't recall) to get each's infinite sum, and add them up!