Write an ML function sum which, given an integer n computes the sum of the first

Question

Write an ML function sum which, given an integer n computes the sum of the first n naturals. Namely, it computes: sigma_i = 0^n i fun sum n = ... Extent your sum function into a sumsq function. Given a natural n, sumsq computes the sum of the squares of the first n naturals: sigma_i = 0^n i^2 fun sumsq n = ... Write an ML function sumOdd which, given a natural n computes the sum of the first n odd naturals. For instance, sumOdd 4 = 1 + 3 + 5 + 7 (i.e., we have four terms). fun sumOdd n = ... Write an ML function fib that computes, from an integer input n, the n^th Fibonacci number (as always, fib(i) = fib(i - 1) + fib(i - 2), fib(0) = 0, fib(1) = 1). fun fib n = ... Write an ML function fibFast that computes, in linear time, from an integer input n, the n^th Fibonacci's number. fun fibFast n = ...

Explanation / Answer

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fun f = FibFast(n)

% Returns the nth number in the Fibonacci sequence.

F=zeros(1,n+1);

F(2) = 1;

for i = 3:n+1

F(i) = F(i-1) + F(i-2);

end

f = F(n);

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