The sum of....

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Q1.
a/[(a + 1)(a + 2)] = 2/(a+ 2) - 1/(a +1).
For a = 1, 1st term = [2/3 - 1/2]2 = 4/3 - 1.
For a = 2, 2nd term = [2/4 - 1/3]2^2 = 2 - 4/3.
For a = 3, 3rd term = [2/5 - 1/4]2^3 = 16/5 - 2.
So you can see that the terms cancelled out leaving -1 and + 16/5. When continuing the process,
For a = n-1, (n-1)th term = [2/(n+1) - 1/n]2^(n-1) = 2^n/(n+1) - 2^(n-1)/n.
For a = n, nth term = [2/(n+2) - 1/(n + 1)]2^n = 2^(n+1)/(n+2) - 2^n/(n+1).
So the answer is -1 + 2^(n+1)/(n+2).
Q2.
This is a simple G.S., so answer is obvious.