(1 point) match each of the following with the correct statement. a. the series is absolutely convergent. c. the series converges, but is not absolutely convergent. d. the series diverges. c 1. ∑n=1[infinity](−1)n+1(9+n)4n(n2)42n d 2. ∑n=1[infinity](n42−6n3)n d 3. ∑n=1[infinity](n+1)n5n2 d 4. ∑n=1[infinity](n+1)n5n d 5. ∑n=1[infinity](−1)nn−2ln(n+6) d 6. ∑n=1[infinity](−5n)nn5n

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!