SOLUTION: Compute the sum
(2)/(1*2*3) + (2)/(2*3*4) + (2)/(3*4*5) + ...
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Question 1035833: Compute the sum
(2)/(1*2*3) + (2)/(2*3*4) + (2)/(3*4*5) + ...
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
+...
By partially decomposing the fraction, it is easy to see that
.
==> The partial sum up to the nth term is as follows:
+
+
+
+
+
..................
+
+
.
The effect of arranging the sum this way is, it becomes easy to see that diagonal "like" terms cancel each other, and what remains after the telescoping is the expression
.
Therefore, letting n approach infinity, we obtain
+... = .
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