How to write the summation of the maclaurin series of cos(x)?

How to write the summation of Maclaurin series of cos(x)?

I tried:

>> syms k x

>> SUM = symsum((-1).^(k+1) * x.^2*(k+1) / factorial(2*(k+1)), k, 0, (k+1))

% I used S = symsum(f, k, a, b) formula

I need to calculate the sum of the k+1 terms with an input of k

(k is a script which has the expression: >>k = input('enter an integer: ')

I tried it and everything is working until the last step. When all the numbers are defined, the formula didn't give me a number. Instead, I got this:

>>SUM =

x^2*symsum(((-1)^(m + 1)*(m + 1))/factorial(2*m + 2), m, 0, m + 1)

Any thoughts on how can I change my code?

[Jan]

Please post the original code and use the "{} Code" button for formatting. Currently it is not clear, if "m" is declared as symbolic variable also. Do you want a symbolic expression at all? What about calculating the sum numerically?

[Ariel Chou]

So the question asks us to:

1. generate a real number x in the range from 0 to 2π

2. prompt the user to enter a non-negative integer m

3. call a function fsum that will evaluate the sum of the m+1 terms of the maclaurin series of cos(x)

Right now I typed:

>> low=0;

>>high = 2*pi;

>> x = rand*(high-low)+low;

>> m = round(abs(input('Enter a non negative integer:')))

>> syms m x

>> fsum = symsum ((-1).^(m+1) * x.^2*(m+1) / factorial(2*(m+1)), m, 0, m+1))

Answer 1

[Jan]

The MacLaurin series of cos() is:

cos(x) := Sum(i = 0 to Inf) [((-1)^i / (2*i)!) * x ^ (2*i)]

[EDITED, "2*i!" replaced by "(2*i)!"]

If you want a numerical output, it is the direct approach to calculate it numerical directly:

function y = cosMacLaurin(x, k)
S = 0;
for i = 0:k
  S = S +  ...
end
end

I leave the "..." up to you, because I assume that this is a homework question.

[Stephen23]

+1 nice and clear

[Ariel Chou]

So to calculate the sum of k+1 terms of the series, do I just change k to k+1?

[Jan]

@Arial: You start at i = 0. The list 0,1,2,...,k has k+1 elements, such that the shown loop has k+1 terms already.

Answer 2

[Arun Kanchibotla]

Hey, I have been trying to do something similar and I am getting the same result. symsum(((-1)^m*(6407787516743315/1125899906842624)^(2*m))/factorial(2*m), m, 0, m) However, I am expecting an integer number. What am I supposed to do to correct this?

[Ariel Chou]

I got the same results as well

[Karan Gill]

Post your code and in a separate question. Without code, we can't help.

[Jan]

Please open a new thread for a new question. Then explain, which result you get, and which you expect. Perhaps only the expectation is the problem.