SOLUTION: Prove than sum(1/(r^2),r=1,n)is greater than or equal to 2- (1/n) for n is greater than or equal to 1. Thanks!!

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Question 827159: Prove than sum(1/(r^2),r=1,n)is greater than or equal to 2- (1/n) for n is greater than or equal to 1.
Thanks!!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
cross%28%28sum%281%2Fr%5E2%2Cr=1%2Cn%29%29%3E=2-1%2Fn%29

This is not true!

Although equality holds for n=1:

1%2F1%5E2%22%22=%22%221
2-1%2F1%22%22=%22%221

It isn't true for n=2 or greater, for when n=2

1%2F1%5E2%2B1%2F2%5E2%22%22=%22%221%2B1%2F4%22%22=%22%221.25
yet
2-1%2F2%22%22=%22%221.5, %22%22%3C=%22%22 holds but not %22%22%3E=%22%22

And when n=3

1%2F1%5E2%2B1%2F2%5E2%2B1%2F2%5E3%22%22=%22%221%2B1%2F4%2B1%2F8%22%22=%22%221.375
yet
2-1%2F3%22%22=%22%221.666667, again %22%22%3C=%22%22 holds but not %22%22%3E=%22%22.

Euler proved in 1735 that the the sum on the left approaches the irrational
number pi%5E2%2F6 = 1.6449340668482264... and it is an increasing function, so it
is always less that pi%5E2%2F6.

The expression on the right is also increasing, and approaches 2.  But
beginning with the third term it is already larger than the left side can 
ever be!

Edwin