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
)

I'm guessing the sum is supposed to be

Split the summand into partial fractions:

If , then

If , then

This means

Consider the th partial sum of the series:

The sum telescopes so that

and as , the second term vanishes and leaves us with

4x and 6y

im not sure though

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!