For the following telescoping series, find a formula for the nth term of the sequence of partial sums
S
n
. Then evaluate
lim
n
→
[infinity]
S
n
to obtain the value of the series or state that the series diverges.

∑
[infinity]
k
=
1
=
10
(
5
k
−
1
)
(
5
k
+
4
)

Sophia wrote an equation to represent the revenue of a movie theater for one day. she let x represent the number of child tickets sold and y represents the nunver of adult tickets sold. if a child ticket cost $4, an adult ticket cost $6, and the total revenue for the daybwas $420, which equation could sophia use to represent the number of chikd and adult tickets that were sold?