Translation examples
Kirjan idea perustuu Choose Your Own Adventure -kirjasarjan formaattiin, jossa lukija valitsee vaihtoehdoista seikkailun kulun.
They are formatted like the popular Choose Your Own Adventure books, where the reader makes decisions that change the outcome of the story.
Lauseen mukaan on mahdollista kehittää mikä tahansa potenssi (x + y):n summaksi, joka on muotoa ( x + y ) n = ( n 0 ) x n y 0 + ( n 1 ) x n − 1 y 1 + ( n 2 ) x n − 2 y 2 + ⋯ + ( n n − 1 ) x 1 y n − 1 + ( n n ) x 0 y n , {\displaystyle (x+y)^{n}={n \choose 0}x^{n}y^{0}+{n \choose 1}x^{n-1}y^{1}+{n \choose 2}x^{n-2}y^{2}+\cdots +{n \choose n-1}x^{1}y^{n-1}+{n \choose n}x^{0}y^{n},} missä jokainen ( n k ) {\displaystyle {\tbinom {n}{k}}} on tietty positiivinen kokonaisluku, joka tunnetaan binomikertoimena.
According to the theorem, it is possible to expand any power of x + y into a sum of the form ( x + y ) n = ( n 0 ) x n y 0 + ( n 1 ) x n − 1 y 1 + ( n 2 ) x n − 2 y 2 + ⋯ + ( n n − 1 ) x 1 y n − 1 + ( n n ) x 0 y n , {\displaystyle (x+y)^{n}={n \choose 0}x^{n}y^{0}+{n \choose 1}x^{n-1}y^{1}+{n \choose 2}x^{n-2}y^{2}+\cdots +{n \choose n-1}x^{1}y^{n-1}+{n \choose n}x^{0}y^{n},} where each ( n k ) {\displaystyle {\tbinom {n}{k}}} is a specific positive integer known as a binomial coefficient.
Albumilla The Offspring alkoi väistyä Epitaphin yhtyeille tyypillisistä poliittisesti kantaa ottavista punk-teemoista, ja lähestyi valtavirran rockia lauluilla kuten "All I Want", "Gone Away" ja "I Choose".
The album saw the band move away from the political-punk themes common to many Epitaph bands, and more into mainstream rock with songs like: "Gone Away" and "I Choose".
Kun lukujono pk määritellään p n k = ( n + k − 1 k − 1 ) {\displaystyle p_{n}^{k}={n+k-1 \choose k-1}} on Cesàron summan määritelmä Ck(s) = N(pk)(s).
Here, if we define the sequence pk by p n k = ( n + k − 1 k − 1 ) {\displaystyle p_{n}^{k}={n+k-1 \choose k-1}} then the Cesàro sum Ck is defined by Ck(s) = N(pk)(s).
Käytettäessä summamerkintää se voidaan kirjoittaa ( x + y ) n = ∑ k = 0 n ( n k ) x n − k y k = ∑ k = 0 n ( n k ) x k y n − k . {\displaystyle (x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}y^{k}=\sum _{k=0}^{n}{n \choose k}x^{k}y^{n-k}.} Viimeinen lauseke seuraa edellisestä ja on symmetrinen x :n ja y :n ensimmäisen lausekkeen kanssa, ja verrattaessa kertoimiin huomataan, että binomikertoimien jono kaavassa on myös symmetrinen.
Using summation notation, it can be written as ( x + y ) n = ∑ k = 0 n ( n k ) x n − k y k = ∑ k = 0 n ( n k ) x k y n − k . {\displaystyle (x+y)^{n}=\sum _{k=0}^{n}{n \choose k}x^{n-k}y^{k}=\sum _{k=0}^{n}{n \choose k}x^{k}y^{n-k}.} The final expression follows from the previous one by the symmetry of x and y in the first expression, and by comparison it follows that the sequence of binomial coefficients in the formula is symmetrical.
Love Gun Deuce Makin' Love Lick It Up Christine Sixteen She Tears Are Falling Got to Choose I Love It Loud Love Her All I Can I Want You Parasite War Machine 100,000 Years Unholy Shout It Out Loud I Was Made for Lovin' You Detroit Rock City God Gave Rock & Roll To You II Rock and Roll All Nite Tämä musiikkiin liittyvä artikkeli on tynkä.
Disc one: "Love Gun" "Deuce" "Makin' Love" "Lick It Up" "Christine Sixteen" "She" "Tears Are Falling" "Got To Choose" "I Love It Loud" "Love Her All I Can" "I Want You" "Parasite" Disc two: "War Machine" "100,000 Years" "Unholy" "Shout It Out Loud" "I Was Made for Lovin' You" "Detroit Rock City" "God Gave Rock 'N' Roll to You II" "Rock and Roll All Nite" "American video certifications – Kiss – Rock the Nation Live".
Luvut ovat nimetty belgialaisen matemaatikon Eugène Charles Catalanin mukaan. n:s Catalanin luku lasketaan binomikertoimilla seuraavasti: C n = 1 n + 1 ( 2 n n ) = ( 2 n ) ! ( n + 1 ) ! n ! kun n ≥ 0. {\displaystyle C_{n}={\frac {1}{n+1}}{2n \choose n}={\frac {(2n)!}{(n+1)!\,n!}}\qquad {\mbox{ kun }}n\geq 0.} Ensimmäiset Catalanin luvut ovat (n arvoilla 0, 1, 2..): 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, … Tämä matematiikkaan liittyvä artikkeli on tynkä.
The nth Catalan number is given directly in terms of binomial coefficients by C n = 1 n + 1 ( 2 n n ) = ( 2 n ) ! ( n + 1 ) ! n ! = ∏ k = 2 n n + k k for n ≥ 0. {\displaystyle C_{n}={\frac {1}{n+1}}{2n \choose n}={\frac {(2n)!}{(n+1)!\,n!}}=\prod \limits _{k=2}^{n}{\frac {n+k}{k}}\qquad {\text{for }}n\geq 0.} The first Catalan numbers for n = 0, 1, 2, 3, ... are 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452, ... (sequence A000108 in the OEIS).
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