how do you rewrite or find the answer? rite s in expanded form, you sometimes se

Question

how do you rewrite or find the answer?

rite s in expanded form, you sometimes see that all the terms cancel except the first Successive cancellation of terms collapses the sum like a telescope. In certain sums each term is a difference of two quantities. When you wi and A Telescoping Sum Some sums can be transformed into telescoping sums, which then can be simple expression. For instance, observe that = -k(k+1) k(k + 1) xo -) k k+1 ri Use this identity to find a simple expression for RR + D ! Other recursively defined sequences are discussed later in this section and, Section 5.6. in greater

Explanation / Answer

We have 1/k – 1/(k+1) = 1/k(k+1) . Therefore, k=1n 1/ k(k+1) = k=1n (1/k) - k=1n (1/k+1) = 1 + k=2n (1/k) – [k=2n (1/k) + 1/(n+1)] = 1-1/(n+1) = n/(n+1).

Thus, the answer is n/(n+1).

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