Programming Taskbook 4

[Introduction] [About input-output operations] [Input-output and assignment] [Integers] [Logical expressions] [Conditional statement] [Selection statement] [Loop with the parameter] [Loop with the condition] [Numerical sequences] [Procedures and functions] [Minimums and maximums] [One-dimensional arrays] [Two-dimensional arrays (matrices)] [Characters and strings] [Binary files] [Text files] [Structured data types in procedures and functions] [Recursion] [Dynamic data structures] [Dynamic data structures (.NET)]

Loop with the parameter

For1. Given integers K and N (N > 0), output the number K N times.

For2. Given two integers A and B (A < B), output in ascending order all integers in the range A to B (including A and B). Also output the amount N of these integers.

For3. Given two integers A and B (A < B), output in descending order all integers in the range A to B (excluding A and B). Also output the amount N of these integers.

For4. Given the price of 1 kg of sweets (as a real number), output the cost of 1, 2, … , 10 kg of these sweets.

For5°. Given the price of 1 kg of sweets (as a real number), output the cost of 0.1, 0.2, … , 1 kg of these sweets.

For6. Given the price of 1 kg of sweets (as a real number), output the cost of 1.2, 1.4, … , 2 kg of these sweets.

For7. Given two integers A and B (A < B), find the sum of all integers in the range A to B inclusive.

For8. Given two integers A and B (A < B), find the product of all integers in the range A to B inclusive.

For9. Given two integers A and B (A < B), find the sum of squares of all integers in the range A to B inclusive.

For10. Given an integer N (> 0), find the value of a following sum (as a real number):

1 + 1/2 + 1/3 + … + 1/N.

For11. Given an integer N (> 0), find the value of a following sum (as an integer):

N² + (N + 1)² + (N + 2)² + … + (2·N)².

For12°. Given an integer N (> 0), find the value of a following product of N factors:

1.1 · 1.2 · 1.3 · … .

For13°. Given an integer N (> 0), find the value of the following expression of N terms with alternating signs:

1.1 – 1.2 + 1.3 – … .

Do not use conditional statements.

For14. Given an integer N (> 0), compute N² by means of the formula

N² = 1 + 3 + 5 + … + (2·N – 1).

Output the value of the sum after addition of each term. As a result, squares of all integers in the range 1 to N will be output.

For15°. Given a real number A and an integer N (> 0), find A raised to the power N (i. e., the product of N values of A):

A^N = A·A· … ·A.

For16°. A real number A and an integer N (> 0) are given. Using one loop-statement compute and output powers A^K for all integer exponents K in the range 1 to N.

For17. A real number A and an integer N (> 0) are given. Using one loop-statement compute the sum

1 + A + A² + A³ + … + A^N.

For18. A real number A and an integer N (> 0) are given. Using one loop-statement compute the expression

1 – A + A² – A³ + … + (–1)^N·A^N.

Do not use conditional statements.

For19°. Given an integer N (> 0), find the value of a following product:

N! = 1·2·…·N

(N–factorial). To avoid the integer overflow, compute the product using a real variable and output the result as a real number.

For20°. An integer N (> 0) is given. Using one loop-statement compute the sum

1! + 2! + 3! + … + N!,

where N! (N–factorial) is the product of all integers in the range 1 to N: N! = 1·2·…·N. To avoid the integer overflow, compute the sum using real variables and output the result as a real number.

For21. An integer N (> 0) is given. Using one loop-statement compute the sum

1 + 1/(1!) + 1/(2!) + 1/(3!) + … + 1/(N!),

where N! (N–factorial) is the product of all integers in the range 1 to N: N! = 1·2·…·N. The result is an approximate value of the constant e = exp(1).

For22. A real number X and an integer N (> 0) are given. Compute the expression

1 + X + X²/(2!) + … + X^N/(N!)

(N! = 1·2·…·N). The result is an approximate value of exp(X).

For23. A real number X and an integer N (> 0) are given. Compute the expression

X – X³/(3!) + X⁵/(5!) – … + (–1)^N·X^2·N+1/((2·N+1)!)

(N! = 1·2·…·N). The result is an approximate value of sin(X).

For24. A real number X and an integer N (> 0) are given. Compute the expression

1 – X²/(2!) + X⁴/(4!) – … + (–1)^N·X^2·N/((2·N)!)

(N! = 1·2·…·N). The result is an approximate value of cos(X).

For25. A real number X (|X| < 1) and an integer N (> 0) are given. Compute the expression

X – X²/2 + X³/3 – … + (–1)^N–1·X^N/N.

The result is an approximate value of ln(1 + X).

For26. A real number X (|X| < 1) and an integer N (> 0) are given. Compute the expression

X – X³/3 + X⁵/5 – … + (–1)^N·X^2·N+1/(2·N+1).

The result is an approximate value of atan(X).

For27. A real number X (|X| < 1) and an integer N (> 0) are given. Compute the expression

X + 1·X³/(2·3) + 1·3·X⁵/(2·4·5) + … +
+ 1·3·…·(2·N–1)·X^2·N+1/(2·4·…·(2·N)·(2·N+1)).

The result is an approximate value of asin(X).

For28. A real number X (|X| < 1) and an integer N (> 0) are given. Compute the expression

1 + X/2 – 1·X²/(2·4) + 1·3·X³/(2·4·6) – … +
+ (–1)^N–1·1·3·…·(2·N–3)·X^N/(2·4·…·(2·N)).

The result is an approximate value of the square root of 1 + X.

For29. An integer N (> 1) and two points A, B (A < B) on the real axis are given. The segment [A, B] is divided into N sub-segments of equal length. Output the length H of each sub-segment and then output the sequence of points

A, A + H, A + 2·H, A + 3·H, … , B,

which forms a partition of the segment [A, B].

For30. An integer N (> 1) and two points A, B (A < B) on the real axis are given. The segment [A, B] is divided into N sub-segments of equal length. Output the length H of each sub-segment and then output the values of a function F(X) = 1 – sin(X) at points dividing the segment [A, B]:

F(A), F(A + H), F(A + 2·H), … , F(B).

For31. An integer N (> 0) is given. A sequence of real numbers A_K is defined as:

A₀ = 2, A_K = 2 + 1/A_K–1, K = 1, 2, … .

Output terms A₁, A₂, … , A_N of the sequence.

For32. An integer N (> 0) is given. A sequence of real numbers A_K is defined as:

A₀ = 1, A_K = (A_K–1 + 1)/K, K = 1, 2, … .

Output terms A₁, A₂, … , A_N of the sequence.

For33°. An integer N (> 0) is given. An integer-valued sequence of the Fibonacci numbers F_K is defined as:

F₁ = 1, F₂ = 1, F_K = F_K–2 + F_K–1, K = 3, 4, … .

Output terms F₁, F₂, ..., F_N of the sequence.

For34. An integer N (> 1) is given. A sequence of real numbers A_K is defined as:

A₁ = 1, A₂ = 2, A_K = (A_K–2 + 2·A_K–1)/3, K = 3, 4, … .

Output terms A₁, A₂, … , A_N of the sequence.

For35. An integer N (> 2) is given. A sequence of integers A_K is defined as:

A₁ = 1, A₂ = 2, A₃ = 3, A_K = A_K–1 + A_K–2 – 2·A_K–3, K = 4, 5, … .

Output terms A₁, A₂, … , A_N of the sequence.

Nested loops

For36°. Given positive integers N and K, find the sum

1^K + 2^K + … + N^K.

To avoid the integer overflow, compute the sum using real variables and output the result as a real number.

For37. Given an integer N (> 0), find the sum

1¹ + 2² + … + N^N.

To avoid the integer overflow, compute the sum using real variables and output the result as a real number.

For38. Given an integer N (> 0), find the sum

1^N + 2^N–1 + … + N¹.

To avoid the integer overflow, compute the sum using real variables and output the result as a real number.

For39. Positive integers A and B (A < B) are given. Output all integers in the range A to B, with an integer of a value K being output K times (for example, the number 3 must be output 3 times).

For40. Integers A and B (A < B) are given. Output all integers in the range A to B, with the number A being output once, the number A + 1 being output twice, and so on.

Date of page creation: 01.03.2007.