Q.34
[tex]\sum\limits_{k=1}^{\infty}420\left(1.002\right)^{k-1} [/tex]
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
[tex] \sum\limits_{k=1}^{\infty}-5\left(\dfrac{4}{5}\right)^{k-1} [/tex]
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 :
[tex]S=\dfrac{a_1}{1-r}[/tex]
We have:
[tex]a_1=-5\left(\dfrac{4}{5}\right)^{1-1}=-5\left(\dfrac{4}{5}\right)^0=-5\\\\r=\dfrac{4}{5}[/tex]
substitute:
[tex]S=\dfrac{-5}{1-\frac{4}{5}}=-\dfrac{5}{\frac{1}{5}}=-5\cdot\dfrac{5}{1}=-25[/tex]
Answer: c. Converges, -25.
