Question

Please help me right away with these problems.

Answer 1

Q.34

`\sum\limits_(k=1)^(\infty)420\left(1.002\right)^(k-1)`

The infinite geometric series is converges if |r| < 1.

We have r =1.002 > 1, therefore our infinite geometric series is Diverges

Answer: c. Diverges, sum not exist.

Q.35

`\sum\limits_(k=1)^(\infty)-5\left((4)/(5)\right)^(k-1)`

The infinite geometric series is converges if |r| < 1.

We have r = 4/5 < 1, therefore our infinite geometric series is converges.

The sum S of an infinite geometric series with |r| < 1 is given by the formula :

`S=(a_1)/(1-r)`

We have:

`a_1=-5\left((4)/(5)\right)^(1-1)=-5\left((4)/(5)\right)^0=-5\\\\r=(4)/(5)`

substitute:

`S=(-5)/(1-(4)/(5))=-(5)/((1)/(5))=-5\cdot(5)/(1)=-25`

Answer: c. Converges, -25.