What are the values of these sums, where S={1,3,5,7}?
∑(jϵS) j
∑(jϵS) j²
∑(jϵS) (1/j)
∑(jϵS) 1

Solution:

a.) ∑(jϵS) j [Sum]

1+3+5+7=16

1+3+5+7=16

b.) ∑(jϵS) j² [Sum of squares]

1^2+3^2+5^2+7^2=1+9+25+49=84

12+3²+5²+7²

=1+9+25+49=84

c.) ∑(jϵS) (1/j)

1/1+1/3+1/5+1/7=

By taking the LCM of the denominators

105/105 + 35/105 + 21/105 + 15/105=

176/105=1.6762

176/105=1.6762

d.) ∑(jϵS) 1

1+1+1+1=4

1+1+1+1=4

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What are the values of these sums, where S={1,3,5,7}?
∑(jϵS) j
∑(jϵS) j²
∑(jϵS) (1/j)
∑(jϵS) 1

Summary:

The values of the sums ∑(jϵS) j= 16, ∑(jϵS) j²= 84, ∑(jϵS) (1/j)= 1.6762, ∑(jϵS) 1= 4