<p>Hi,</p>
<p>In our calc class we've been studying sigma notation. I understand how to calculate the sums and everything but can't figure out the pattern in the sum below. Usually, I can see the patterns fairly quickly, but this one just seems impossible :(
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I need to express the following sum in sigma notation
The sum given is: 7 + (3/2) + (5/9) + (1/4) + (3/25)
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I feel like I tried everything, but still can't figure it out :(</p>
<p>Thanks in advance:)</p>
<p>Got it. that was fun :D</p>
<p>Sigma(n=1) [(8-n)/n^2]</p>
<p>The denominators gave it away.. 2, 9, 4, 25..</p>
<p>Wow, thanks! I got all the others, but that one was hard. Do you know if there's like a process to finding the patterns? Usually, I just try to guess :(</p>
<p>Thanks again :)</p>
<p>There isn't really a set process.. you just have to look at it and try different things... look at the numerators: 7, 3(goes evenly into 6), 5, 1(goes evenly into 4), 3.. see that? Then you can manipulate them to get the top to read 7,6,5,4,3:</p>
<p>7/1, 6/(2<em>2), 5/9, 4/(4</em>4), 3/25.. I actually saw the pattern from the denominators, then manipulated, then saw the countdown on top.. you just gotta try stuff :)</p>