Square root algorithm.\ a. Let

p_(0)=2

and define

p_(n+1)=(p_(n))/(2)+(1)/(p_(n))

for

n=0,1,2,dots

. Create a table showing

n

versus

p_(n)

for

n=0,1,2,3,4,5

. Notice the rapid convergence towards

\\\\sqrt(2)

.\ b. Let

p_(0)=3

and define

p_(n+1)=(p_(n))/(2)+(3)/(2n)

for

n=0,1,2,dots

. Create a table showing

n

a. Let p0=2 and define pn+1=2pn+pn1 for n=0,1,2,. Create a table showing n versus pn for n=0,1,2,3,4,5. Notice the rapid convergence towards 2. b. Let p0=3 and define pn+1=2pn+2n3 for n=0,1,2,. Create a table showing n