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Sum of series

a(n) = n^2 - (n-1)^2 find the summation of the series upto n i.e. a(1)+a(2)+...+a(n)

3 months ago

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Sum of series VI

What is the sum of the following sequence: Σk⋅k! for k=1...n for different n?

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Sum of series V

What is the sum of the following sequence: Σk(k+1) for k=1...n for different n?

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Sum of series IV

What is the sum of the following sequence: Σ(-1)^(k+1) (2k-1)^2 for k=1...n for different n?

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Sum of series III

What is the sum of the following sequence: Σ(2k-1)^3 for k=1...n for different n?

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Sum of series II

What is the sum of the following sequence: Σ(2k-1)^2 for k=1...n for different n?

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Sum of series I

What is the sum of the following sequence: Σ(2k-1) for k=1...n for different n?

3 months ago

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Prime Ladders

A <http://en.wikipedia.org/wiki/Word_ladder word ladder> transforms one word to another by means of single-letter mutations. So ...

3 months ago

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Goldbach's marginal conjecture - Write integer as sum of three primes

Goldbach's strong conjecture states that every even integer greater than 2 can be expressed as the sum of two primes. For exampl...

3 months ago

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Twins in a Window

<http://en.wikipedia.org/wiki/Twin_primes Twin primes> are prime numbers that differ by 2, such as [11,13] or [41,43]. Write a f...

3 months ago

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Twin Primes

Twin primes are pairs of primes that are immediately next to each other (difference of two). The lesser of twin primes are 3, 5,...

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Numbers spiral diagonals (Part 2)

Inspired by Project Euler n°28 and 58. A n x n spiral matrix is obtained by starting with the number 1 and moving to the right ...

3 months ago

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Perimeter of a semicircle

Given the diameter d, find the perimeter of a semicircle

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Given a square and a circle, please decide whether the square covers more area.

You know the side of a square and the diameter of a circle, please decide whether the square covers more area.

3 months ago

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Approximation of Pi

Pi (divided by 4) can be approximated by the following infinite series: pi/4 = 1 - 1/3 + 1/5 - 1/7 + ... For a given number of...

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Pi Estimate 1

Estimate Pi as described in the following link: <http://www.people.virginia.edu/~teh1m/cody/Pi_estimation1.pdf>

3 months ago

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(Linear) Recurrence Equations - Generalised Fibonacci-like sequences

This problem is inspired by problems <http://uk.mathworks.com/matlabcentral/cody/problems/2187-generalized-fibonacci 2187>, <htt...

3 months ago

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Fibonacci Decomposition

Every positive integer has a unique decomposition into nonconsecutive Fibonacci numbers f1+f2+ ... Given a positive integer n, r...

3 months ago

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How many Fibonacci numbers?

Find the number of unique Fibonacci numbers (don't count repeats) in a vector of positive integers. Example: x = [1 2 3 4...

3 months ago

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Return fibonacci sequence do not use loop and condition

Calculate the nth Fibonacci number. Given n, return f where f = fib(n) and f(1) = 1, f(2) = 1, f(3) = 2, ... Examples: ...

3 months ago

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Find the next Fibonacci number

In the sequence of Fibonacci numbers, every number is the sum of the two preceding ones: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...

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Laws of motion 4

Given the initial velocity 'u', final velocity 'v' and acceleration 'a', find the distance travelled.

3 months ago