sum of sigma?

Question

7
Σ (i^2 + i)
i=3

i would not know how to find the answer unless i wrote it all out. (3^2 + 3) + (4^2 + 4) + .... (7^2 + 4) = sum

what I do know that if the problem were i=1 instead of 3..I would just use the formulas for i^2 and i

n(n+1)(2n+1)/6 and n(n+1)/3

would i still somehow be able to use these formulas to answer this problem?

i wrote (7^2 + 4)

i meant 7, not 4

also, the formula for i is n(n+1)/2....not divided by 3

Answer 1

i'm not really sure what you are asking, but you are doing it correct...

not following you on the rest of your question..

Answer 2

you can rearrange this question as

7
Σ (i^2 + i)
i=1
-

2
Σ (i^2 + i)
i=1

now u can use the formula

Answer 3

7
Σ (i^2 + i)=
i=3


7
Σ i^2 +
i=3


7
Σ i
i=3

=7(8)15/6 - 5

+

7(8)/2 - 3

=135+25=160

Answer 4

Σ {i = 3 ~ 7} = Σ {i = 1 ~ 7} - Σ {i = 1 ~ 2}