Question

is the summation from i=n+1 to 3n the same as the summation from i=1 to 4n?

Answer 1

\[\sum_{n+1}^{3n} an=\sum_1^{4n}an\]

Answer 2

i can't imagine why they would be the same

Answer 3

if n = 10, on the first case you'll have (10+1) to 3*10 = 11 to 30 = 19.
on the second case you'll have 1 to 40 = 39.. So the summation is diferent

Answer 4

\[\sum_{j=n+1}^{5n}\] what does this simplify to then? Would it simplify to: \[\sum_{j=1}^{5n-1}\]?

Answer 5

If you subtract 1 on the up function, then you must subtract 1 on the down function.
Something like:

\[\sum_{i=n}^{5n-1}\]