Plz help First person gets brainliest :)
Plz no fake answers!

Wow this hard

Step-by-step explanation:

X∞

k=1

k(k + 2)

(k + 3)2

is convergent or divergent. If it is convergent, find its sum.

This series diverges. To see this, I will show that the terms in the sequence do not

go to zero:

lim

k→∞

k(k + 2)

(k + 3)2

= lim

k→∞

k

2 + 2k

k

2 + 6k + 9

.

Dividing numerator and denominator by k

2 yields

lim

k→∞

1

k

2

1 + 2

k

1

k

2

1 + 6

k +

9

k

2

= lim

k→∞

1 + 2

k

1 + 6

k +

9

k

2

= 1.

Therefore, using the nth term test (a.k.a. Test for Divergence), the series diverges

idn

step-by-step explanation: