Express the given sums using sigma notation. 1/2+1/2×3+1/3×4+...1/99×100?
just write what they gave you
99
∑ 1/(k(k+1))
k=1
To express the given sums using sigma notation, we need to find a pattern in the terms of the series.
Let's observe the terms of the series:
1/2, 1/2 * 3, 1/3 * 4, ...
We notice that each term has the form 1/n * (n+1). The denominator of the fraction starts from 2 and increases by 1 with each term, while the numerator is always the next consecutive number.
Now that we have identified the pattern, we can write the series using sigma notation.
We start with the index, which will be represented by the variable k, and it will go from 1 to 99 since there are 99 terms in the series.
The general term of the series is 1/k * (k+1), which represents each term in the series.
Using sigma notation, the expression for the given series can be written as:
Σ [1/k * (k+1)] from k = 1 to 99