sigma help: 1/1 + 1/4 + 1/9 + 1/16 + ... + 1/36

[yummymummy1713]

1/1 + 1/4 + 1/9 + 1/16 + ... + 1/36

on top is the 1/36 and k= 1/1

I recognize the pattern is that the bottom is going up by odd numbers. The numerator is 1. How would I express the denominator?

Thanks!

 

[daon]

With n=6, your series is:
\(\displaystyle \L \sum _{i=1}^{n} \frac{1}{i^2}\)

Incase you care, the limit as n -> infinity is \(\displaystyle \frac{\pi ^2}{6}\). I mention this only because my class just covered this

 

[yummymummy1713]

why is 6 on the top of the sigma sign?

 

[daon]

The 6 on top tells you to stop adding when i=6.

So the sum is equal to: 1/1² + 1/2² + 1/3² + 1/4² + 1/5² + 1/6²

 

[skeeter]

6 is on top because that is the value of n for which the summation ends

\(\displaystyle \L \sum _{i=1}^{6} \frac{1}{i^2} = \frac{1}{1^2} + \frac{1}{2^2} +\frac{1}{3^2} +\frac{1}{4^2} +\frac{1}{5^2} +\frac{1}{6^2}\)