A sequence is defined as: U(n+1) = 1/U(n) where U(1)=2/3. Find the sum from r=(1-100) for U(r)
Un+1=1/Un where U1= 2/3First of all, we need to find U2 and U3 and so on, up until we notice a pattern in the answers. U2 = 1/(2/3) = 3/2U3 = 1/(3/2) = 2/3As we can see, U1 and U3 are equal, and so we know that for every 'n' that is odd, Un will equal 2/3. This is similar for ever 'n' that even where Un will equal 3/2.Therefore in total for this summation, there will be 50 lots of '2/3' and 50 lots of '3/2' so the answer will be 50(2/3) + 50(3/2) = 325/3
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