Which geometric series converges?

0.02+0.02+0.02+0.02+...

4+0.08 +0.0016+0.000032+

4+80+ 1.600+ 32,000+.

0.02+0.04+0.08+0.16+.

4+0.08 +0.0016+0.000032+

Step-by-step explanation:

a+ar+ar²+ar³+ar⁴+…

the  geometric series converges if  |r| < 1

The geometric series converges:

4+0.08 +0.0016+0.000032+

0.08=4*0.02

0.0016=4*(0.02)²

0.000032=4*(0.02)³

r=0.02<1

the co-ordinates of the transformed rectangle are:

d. (0, 0), (0, 3), (-3, 3), (-3, 0)

step-by-step explanation:

from the columns of the given matrix, the co-ordinates of the rectangle before transformation are:

(0, 0), (0, 3), (3, 3), (3, 0)

r =

transformed matrix can be obtained by multiplying the given matrix by r:

columns of the transformed matrix are:

0   0   -3   -3

0   3     3     0

from the columns of the resulted matrix, we can see that the vertices of the transformed triangle are:

(0, 0), (0, 3), (-3, 3), (-3, 0)

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

happy to

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