If t2+t+1=0 , prove (t+1/t)2+(t2+1/t2)2+..+(t27+1/t27)2=54, Mathematics

t=w,w2

L.H.S

(w+w2) + (w2 + w)2 ........

 1  + 1 .....

But every third term is of the form:

(w3n +w3n)2=22

There are nine such terms. Their sum is 36.

The remaining are one. Their sum is 18.

Adding them gives 54.

Posted Date: 3/7/2013 6:24:07 AM | Location : United States







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