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
)

Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 25002500 grams and a standard deviation of 800800 grams while babies born after a gestation period of 40 weeks have a mean weight of 27002700 grams and a standard deviation of 385385 grams. if a 3232-week gestation period baby weighs 21252125 grams and a 4040-week gestation period baby weighs 23252325 grams, find the corresponding z-scores. which baby weighs lessless relative to the gestation period?