Josephood7

Reindex the series to start at k=0k=0
y=∑∞k=4(k+1)xk+3=∑∞k=0y=∑k=4∞(k+1)xk+3=∑k=0∞ 

Find the sum of each of the geometric series given below. For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation.

Let S=∑n=1∞anS=∑n=1∞an be an infinite series such that SN=7−3N2SN=7−3N2.

Consider the series:

a) Determine whether the series is convergent or divergent:  .
(Enter "convergent" or "divergent" as appropriate.)

b) If it converges, find its sum:  .
If the series diverges, enter here "divergent" again.

For both of the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise.

Consider the series

Determine whether the series converges, and if it converges, determine its value.

We might think that a ball that is dropped from a height of 11 feet and rebounds to a height 3/4 of its previous height at each bounce keeps bouncing forever since it takes infinitely many bounces. This is not true! We examine this idea in this problem.

A. Show that a ball dropped from a height hh feet reaches the floor in 14h√14h seconds. Then use this result to find the time, in seconds, the ball has been bouncing when it hits the floor for the first, second, third and fourth times: