Description
Gaussian Sum.
Write a program that computes the sum 1 + 2 + . . . + n for a given positive
integer n. For example, for n = 100, the result is 5050.
Another sum.
Write a program that computes the sum of all even integers between 0 and n.
For instance, for n = 6, the result is 0 + 2 + 4 + 6 = 12.
Prime Factorization.
Write a program that computes the prime factorization of a given posi
tive integer. For instance, the factorization of 60 is 2 ∗ 2 ∗ 3 ∗ 5.
Hints:
- In C++, the modulus function % gives the remainder of integer division, i.e., x is divisible
by y if and only if x%y == 0.
- Given the number n to factorize, iterate through all the numbers i = 2, 3, 4, 5, . . . and check
whether i divides n. If so, print out “i ∗ ” and continue to check the factorization of n/i.
Stop when n cannot be further factorised.
In order to check with CodeJudge, please ensure that (i) the factors are printed in ascending
order, (ii) between two factors print a space, an asterisk (∗), and another space, (iii) and at the
end there is a newline (see example above).
Approximating π. Compute an approximation of π using Leibniz’ formula:
π
4
=
∞
X
i=0
(
−
1)i
2
i
+ 1
= 1 −
1
3
+
1
5
−
1
7
+
1
9
−
1
11
+ . . .
To that end write a function with header double pi(int n) that computes the fifirst n terms
of the infifinite summation (and then multiplies by 4). For instance for n = 1 we get the bad
approximation 4, and with increasing n, the approximation gets better.
