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

$\sum\limits_{k=1}^{\infty}-5\left(\dfrac{4}{5}\right)^{k-1}$

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 :

$S=\dfrac{a_1}{1-r}$

We have:

$a_1=-5\left(\dfrac{4}{5}\right)^{1-1}=-5\left(\dfrac{4}{5}\right)^0=-5\\\\r=\dfrac{4}{5}$

substitute:

$S=\dfrac{-5}{1-\frac{4}{5}}=-\dfrac{5}{\frac{1}{5}}=-5\cdot\dfrac{5}{1}=-25$

Answer: c. Converges, -25.