Question

What are the values of these sums, where S = {1, 3, 5, 7} ?

$\begin{array}{r}\sum _{j\in S} j\\ \sum _{j\in S} j^2\\ \sum _{j\in s} \frac{1}{j}\mid \\ \sum _{j\in S} 1\end{array}$

Short answer

Thus, the values of the sums are given below:

$$\begin{gathered} a)16 \\ b)84 \\ c)\frac{176}{105} \\ d)4 \end{gathered}$$

Step-by-step solution

Step 1:

(a) Given $\sum _{j\in S} j$

Compute the sum of this expression by substituting the values from the set S and adding together.

= 1 + 3 + 5 + 7

= 16

Step 2:

(b) Given : $\sum _{i\in \mathbf{s}} {\mathrm{j}}^2$

Compute the sum of this expression by substituting the values from the set S and adding together.

$\begin{array}{r}=1^2+3^2+5^2+7^2\\ =84\end{array}$

Step 3:

(c) Given : $\sum _{\mathrm{j}\in \mathrm{s}}^1 \frac{1}{\mathrm{j}}$

Compute the sum of this expression by substituting the values from the set S and adding together.

$\begin{array}{r}=\frac{1}{1}+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}\\ =\frac{176}{105}\end{array}$

Step 4:

(d) Given : $\sum _{\mathrm{j}\in \mathrm{S}} 1$

Compute the sum of this expression by substituting the values from the set S and adding together.

= 1 + 1 + 1 + 1

= 4