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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.

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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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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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 BuzzFeed Community

Community Post: The Best Aliases Of Burton "Gus" Guster

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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

Quadratic Sequences Lesson 2 of 7

I designed these lessons to teach my students about quadratic sequences (the 2nd in a series of 7). This lesson focuses on: adding and subtracting binomials, multiplying binomials, calculating the area and perimeter of a rectangle given binomial and monomial side lengths, and finding the GCF's of two expressions with numbers and variables.