Answered: Write the sum using sigma notation: 1 1 1 1 У В, where 1.2 2 -3 3.4 128 · 129 n=1 A B =

Advanced Engineering Mathematics

10th Edition

ISBN: 9780470458365

Author: Erwin Kreyszig

Publisher: Wiley, John & Sons, Incorporated

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Write the sum using sigma notation:
1
1
+...+
1
B. where
1.2
2-3
3.4
128 · 129
n=1
A =
В —

Expert Solution

Step 1

The given sum is $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + \dots + \frac{1}{128 \cdot 129} = \sum_{n = 1}^{A} B$ .

Here notice that every term is in the form of $\frac{1}{n (n + 1)}$ .

For the last term n=128.

So, the value of n varies from 1 to 128.

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