how would you write this sigma notation?

Question

1(3)+2(4)+3(5)+4(6)

Answer 1

1(3)+2(4)+3(5)+4(6) =
1(1 + 2)+2(2 + 2)+3(3 + 2)+4(4 + 2) =
&Sigma n(n+2), where n goes from 1 to 4

->or n goes from 1 to infinity if we have
"1(3)+2(4)+3(5)+4(6) + ..." instead of
"1(3)+2(4)+3(5)+4(6)"

Hope this helps.

Answer 2

S =Sigma from 1 to n ( n(n+2))

Answer 3

Before you write in sigma notation, you have to
find the sequence characteristics, and how they relate to an index. In this case, the coefficients of the term are in a straight arithmetic sequence while the terms in () are also in a straight arithmetic sequence, but offset by +2. So we can summarize
Sum = SIGMA(1 to 4) n(n+2)