Question

Please, I am evaluating an error term y = 5^(n+1)*(n+1) and wish to find the number of terms n required for ln (1.2) to yield an error < 10^-5. The manual computation gave me n > 5. But I need to come out with a MATLAB code with explanations and an output to confirm my manual answer.

function error a = 1.2 - 1; n = 1;

while (1/(n+1) * a^(n+l)) > 10e-6 n = n+1;

end

fprintf ('n = %d is the smallest number of terms needed to get ln (1.2) with an error less than 10^-5\n',n)

n > 5 is the smallest number of terms needed to get In (1.2) with an error less than 10^-5

Please help with line by line explanations, I can't get the output. Don't know what is wrong with the code. Thank you.

Please the error output is less than 10^-5

function error
a=1.5-1;
n=1;
while (1/(n+1)* a^(n+1)) >10e-6
n = n+1;
end
fprintf ('n=% d is the smallest number of terms needed to get ln(1.5) to yield an error less than 10^-5 \n',n)

Answer 1

MATLAB:

function error a = 1.2 - 1; n = 1;
while (1/(n+1) * a^(n+1)) > 10e-6
n = n+1;
end
fprintf ('n = %d is the smallest number of terms needed to get ln (1.2) with an error less than 10^-5\n',n)
N=n
for n=1:N;
y=(1/(n+1) * a^(n+1));
fprintf ('For n = %d ,y=%d\n',n,y)
endfor
end

Command window(output):

n = 6 is the smallest number of terms needed to get ln (1.2) with an error less than 10^-5
N = 6
For n = 1 ,y=0.02
For n = 2 ,y=0.00266667
For n = 3 ,y=0.0004
For n = 4 ,y=6.4e-005
For n = 5 ,y=1.06667e-005
For n = 6 ,y=1.82857e-006