23)    does the following infinite geometric series diverge or converge? explain. 1/7+1/28+1/112+1/448+ it diverges; it has a sum. it converges; it does not have a sum. it diverges; it does not have a sum. it converges; it has a sum.

 The correct option is (D) It converges; it has a sum.

Step-by-step explanation:  We are given to check whether the following infinite geometric series diverge or converge :

We know that

an infinite geometric series converges if the modulus of the common ratio is less than 1.

For the given geometric series, the common ratio r is given by

So, we get

Therefore, the given infinite geometric series converges.

Also, we know that the sum of a convergent infinite geometric series with first term a and common ratio r is given by

For the given series,

Therefore, the required sum will be

Thus, the given series is convergent and it has a sum of

Option (D) is CORRECT.

include a picture of the drawing in order for me to

step-by-step explanation: