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The sums of the reciprocals of the binomial coefficients over successive diagonals in Pascal’s triangle converge into beautiful patterns, apart from the first and second diagonal (which lead to the series 1 + 1 + 1 + 1 + … and the harmonic series, respectively). A proof of the identity can be found on cut-the-knot.org.

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Challenging question on binomial series that students always ask during H2 math tuition.

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from Teachers Pay Teachers

Multiplying Binomials Card Match LEVEL 1 and LEVEL 2 COMBO PACK

Level 1 of my Multiplying Polynomials series is for the introduction to Multiplying Polynomials. Simple basic binomial multiplication allows students to practice their multiplying skills without frustration. Level 2 of my Multiplying Polynomials series is for students who have gained an understanding of FOIL and are ready to practice multiplying binomials with coefficients greater than 1.

from Teachers Pay Teachers

Binomial Theorem Task Cards Quiz Pascal Triangle Posters Bundle

Binomial Theorem with HW, Quiz, Posters, Study Guides, or HandoutsGreat for Algebra or PreCalculus. This bundle of resources and activities is a great addition to the unit containing the Binomial Theorem and Pascals Triangle, usually Sequences and Series.

Three series had been derived by the author, using double-integration in polar co-ordinates, binomial expansion and β & γ-functions for determining the volume, surface-area & perimeter of elliptical-section of oblique frustum of a right circular cone. All these three series are in form of discrete summation of infinite terms which converge into finite values hence these were also named as HCR’s convergence series.

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scientist Sir Isaac Newton. Born on 1643 in Woolsthrope, England, Sir Issac Newton is best known for his law on gravitation. He was a poor student at school or at running the family estate. However, he loved making mechanical toys and models of windmills. Newton explained the theory of gravity and gravitation by inventing calculus as no other principles could explain it. The new revolution in mathematics, Calculus was derived from his binomial theorem to infinite series.

Media: watercolor on Saunders Waterford watercolor paper (300g) Size: 4"x6" Bird Name: Red-Headed Tit or Black-Throated Tit  Binomial Name: Aegithalos Concinnus  Others in the Series:&nbs...

Media: watercolor on Saunders Waterford watercolor paper (300g) Size: 4"x6" Bird Name: Red-Headed Tit or Black-Throated Tit  Binomial Name: Aegithalos Concinnus  Others in the Series: &nb...