Question

d. Use fprintf to tell the user the peak height it lands. onus Question: 2 Questions, 10 points for either Z. Write a for loop or a while loop to determine how many terms are required in the geometric series shown below for it to converge to a value that changes by less than 1e-6 on each iteration. Use fprintf to report to the user how many terms it took and what value it converged to. 2 4 8 16 2n 72 0

Answer 1

As we know the GP series with r<1 can have answer as a/(1-r)

=1/(1-1/2)

=2

To converge means the ans should be 2-0.000001 (i.e. 2-1*e-6)

> ans-rep (99999,1000) >x=2 > sum=0 > ans-rep (99999,1000) > for (i in 1:1000) +if (sum< (2-0.000001)) X X/2 sum=sum+x +elsef + else > print (min(ans)) [1] 22

As shown above the ans converges at 22nd iteration to make the condition false that means by adding 21 values the value converges

Hence we can say that 21 terms are required to converge this series

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