Find the sum to n terms of 1/(1.2.3) + 3/(2.3.4) + 5/(3.4.5) + 7/(4.5.6) +....
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To find the sum of the given series, we need to first identify the pattern in the terms and then apply the appropriate formula.
Looking at the terms of the series, we can see that each term can be written as:
Term(n) = (2n - 1) / (n * (n + 1) * (n + 2)), where n is the position of the term in the series (starting from 1).
Now, to find the sum of the series up to the nth term, we can use the formula for the sum of a series:
Sum(n) = Term(1) + Term(2) + Term(3) + ... + Term(n)
Substituting the expression for Term(n) into the sum formula, we get:
Sum(n) = (2*1 - 1) / (1 * (1 + 1) * (1 + 2)) + (2*2 - 1) / (2 * (2 + 1) * (2 + 2)) + (2*3 - 1) / (3 * (3 + 1) * (3 + 2)) + ... + (2n - 1) / (n * (n + 1) * (n + 2))
Now, we can simplify the expression for each term and then add them up:
Sum(n) = (1 / 6) + (3 / 48) + (5 / 240) + ... + ((2n - 1) / (n * (n + 1) * (n + 2)))
To calculate the sum of the series, we need to specify the value of n.