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.

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b

3030 ur welcome

step-by-step explanation: