Q13/090) if M={x,xy,log(xy)}, N={0,∣x∣ ,y} given: M=N find : ( x + 1/y) + (x^2 + 1/y^2) + (x^3 + 1/y^3) …. + (x^2001 + 1/y^2001)

x and y cannot be zero as we have log(xy) and log zero is undefined .

so we have xy = 1 as log(xy) = 0

as x and y both are positive or –ve.

We have |x| in N . now x = |x| and xy = y => x = y = 1

but x and xy have to be different and |x| and y has to be different

so y = x = - 1 giving M={- 1,1,0 } and N={0, 1 ,0-1}

So x = y =-1 and sum = x^n + 1/y^n = -2 for n = odd and 2 for n = even

So sum = -2 as 1st 1000 pairs cancel leaving with x^2001 + 1/y^2001 = - 2