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.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.