Express the series below in summation notation for the specific number of terms

Question

A.) 0+1+2+3+4+5+6+7+8+9

 

b.) 4+8+12+16+20

 

c.) 6+11+16+21+26+31+36

 

d.) 0+3+8+15+24+35+48+63+80

 

e.) sum of a& e

Answer 1

a)

 

Each consecutive integer is counted by 1.

 

9

 ∑ n

n=0

 

where n=0 is the starting value of n.

 

 

b)

 

The first integer 4 and after that, the count is by 4.

 

4

 ∑ (4n + 4)

n=0

 

 

c)

 

The first integer is 6 and after that, the count is 5.

 

6

 ∑ (5n + 6)

n=0

 

 

 

e)

 

We have       a + e

 

 

e

∑ n

n = a

Answer 2

Part (e) cannot be written as 

e
∑ n .           (*)
n = a

 

It should be written as 

 

Σ_n∈{a,e} n   (**).  

 

An expression like  (*) is ambiguous. In fact, someone who knows the English alphabet could correctly interpret it as saying  a+b+c+d+e.  With (**) any ambiguity has been removed.  Pretty standard in more advanced classes where often one writes things like Σ_n∈A n  and where the set A derives its meaning from the context of the problem at hand.

 

Answer 3

a) ∑(n-1) ; for n= 1 to 10

b) ∑(4n)  ; for n= 1 to 5

c) ∑ (5n+1) ; for n= 1 to 7

d) ∑ (n²-1)  ; for n= 1 to 9

 

e) part question is not clear ..