Find the sum of this: Sn = 1/1x2 + 1/2x3 + 1/3x4 + 1/nx(n+1)
To find the sum of the series Sn = 1/1x2 + 1/2x3 + 1/3x4 + 1/nx(n+1) we need to find a pattern in the series.
Let's rewrite the series as:
Sn = 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + ... + 1/nx(n+1)
We notice that each term in the series is of the form 1/nx(n+1).
We can rewrite the series as follows:
Sn = 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + ... + 1/nx(n+1)
= (1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ... + (1/n - 1/(n+1))
= 1 - 1/(n+1)
= n/(n+1)
Therefore, the sum of the series Sn = n/(n+1).