SIGMA NOTATION
The symbol ∑ is the capital letter for S in the Greek alphabet. It is known as sigma and is the symbol
for the sum of the terms in a sequence.
n
∑ Tₖ
k =1
means T1 + T2 + T3 + T4 + … + Tn and is read as follows: the sum of n terms in the series from T1 to
Tk (different variables such as i, k, m, n, and t are commonly used in the notation, with n often being
the position of the last term.
end with n = 6
6
∑ 5 (3)ⁿ ⁻ⁱ find the sum of all the terms
n =1
sum of from 1 to 6 of the sequence
with the general term 5(3)ⁿ⁻ⁱ
start with n = 1
general term
Determining the number of terms from sigma notation:
TOP – BOTTOM + 1
120 Determining the value of the first term:
Eg: ∑ (2 i−3)
i=15 i starts at 15 – we must substitute 15 in
place of i in the general term in order to
n = 120-15+1 find the value of the first term.
n = 106
T1 = 2(15)-3
T1 = 27
SUM TO INFINITY
An infinite series is said to converge when the series approached a particular value and
diverge when it’s not
Converging series only occurs in the case of a geometric series
A series will only converge if -1 < r < 1 (r = 0)
The symbol ∑ is the capital letter for S in the Greek alphabet. It is known as sigma and is the symbol
for the sum of the terms in a sequence.
n
∑ Tₖ
k =1
means T1 + T2 + T3 + T4 + … + Tn and is read as follows: the sum of n terms in the series from T1 to
Tk (different variables such as i, k, m, n, and t are commonly used in the notation, with n often being
the position of the last term.
end with n = 6
6
∑ 5 (3)ⁿ ⁻ⁱ find the sum of all the terms
n =1
sum of from 1 to 6 of the sequence
with the general term 5(3)ⁿ⁻ⁱ
start with n = 1
general term
Determining the number of terms from sigma notation:
TOP – BOTTOM + 1
120 Determining the value of the first term:
Eg: ∑ (2 i−3)
i=15 i starts at 15 – we must substitute 15 in
place of i in the general term in order to
n = 120-15+1 find the value of the first term.
n = 106
T1 = 2(15)-3
T1 = 27
SUM TO INFINITY
An infinite series is said to converge when the series approached a particular value and
diverge when it’s not
Converging series only occurs in the case of a geometric series
A series will only converge if -1 < r < 1 (r = 0)
