Question

calculate the sum:
5
Σ 3
i=1

Answer 1

what is the first term in the series?

Answer 2

\[\sum_{i=1}^{5}3\]correct?

Answer 3

yes!!

Answer 4

what is the first term in the series?

Answer 5

im not understanding. is it 5?

Answer 6

i?

Answer 7

the first term is 3
every term is 3
there are 5 terms
\(i\) is not in the summand (that's the part after the sigma), so each term is the same
\[\sum_{i=1}^{5}3=5(3)=15\]

Answer 8

to make it more clear perhaps I should write ti more explicitly\[\sum_{i=1}^{5}=3+3+3+3+3=3(1+1+1+1+1)=3(5)=15\] and in general, for any constant \(k\) we could say that\[\sum_{i=1}^{n}k=kn\]