Simplify (-2ab^2b) • (4a^5b^2)

Step-by-step explanation:

okay, to start, lets rewrite this so there are no weird symbols:

so, we are going to multiply the coefficients first. ( -2 times 4)

we get -8. now, when you multiply variables that have exponents, we actually add the exponents. remember it is like terms, so a goes with a and b goes with b.  so, the times would equal . (because a is the same thing as ).

now lets look at b. times would equal . so, because we have multiplied the parentheses, lets look at what we have. we have -8, , and . we need to remember that these were originally multiplied by each other, so we are going to write it that way. . we always write coefficients first, and then the variables in the order of the alphabet. i hope this helps and have a great day!

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}