Question

please write matlab code for these questions in matlabplatform

1, write an m file to determine the sum of the infinite series converges to π2 /6. Do this by computing the sum for a) n-100, b) n-1000 and c) n 10000. Do this by assigning n values using logspace command 2. Write an m-file to evaluate the following algebraic formula log( -a f i>a log) sa where t is a number that a user enters and a 100 3. A problem in timber growth management is to determine how much of an area to leave uncut so that the harvested area is reforested in a certain period of time. It is assumed that reforestation takes place at a known rate per year, depending on climate and soil conditions. A reforestation equation expresses this growth as a function of the amount of timber standing and the reforestation rate. For example, if 100 acres are left standing and the reforestation rate is 0.05, then 100(1+0.05) are forested at the end of the first year. At the end of the second year, the number of acres forested is 105(1+0.05)-110.25 acres Assume that there are 14,000 acres total with 2500 acres uncut and that the reforestation rate is 002 Write a program to calculate and print a table showing the number of acres forested at the end of each year, for up to 20 years

Answer 1

Hello,
          Please find the answer to Q1 attached as under. Please give a thumbs up rating if you find the answer useful! Have a rocking day ahead!

************** Matlab Code **********

n = logspace(2,4,3);
y1 = linspace(1,n(1),n(1));
s1 = sum(1./(y1.^2))
y2 = linspace(1,n(2),n(2));
s2 = sum(1./y2.^2)
y3 = linspace(1,n(3),n(3));
s3 = sum(1./y3.^2)

******** End of Code **********

Output:

s1 =

    1.6350

s2 =

    1.6439

s3 =

    1.6448

You can see that as n increases, the value of the sum converges to pi²/6 (=1.6449)

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