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Useful math formulas for beginners

 1 month ago
source link: https://codeforces.com/blog/entry/128739
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Useful math formulas for beginners

By codepasta, 4 hours ago,

Power of two (bynomial formula):

(a+b)2=a2+b2+2ab(a+b)2=a2+b2+2ab

Useful for proving time-complexity:

1+12+13+14+15+…+1n=log(n)1+12+13+14+15+…+1n=log⁡(n)

Another very useful formula (example problem):

(a+b)(a2+b2)=a4−b4a−b(a+b)(a2+b2)=a4−b4a−b

Sum of first nn numbers:

1+2+3+...+n=n(n−1)21+2+3+...+n=n(n−1)2

Number of ways to choose pair of two numbers from nn elements:

(n2)=n(n+1)2(n2)=n(n+1)2

Another formula:

ak−bk=(a−b)⋅(ak−1b0+ak−2b1+…+a0bk−1)ak−bk=(a−b)⋅(ak−1b0+ak−2b1+…+a0bk−1)

Fibonaci number:

F1=0,F2=1,Fn=Fn−1+Fn−2F1=0,F2=1,Fn=Fn−1+Fn−2

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