Calculus II - Binomial Series Paul's Online Math Notes

Calculus II - Binomial Series Paul's Online Math Notes

Binomial Theorem and Binomial Series : Output.to from Sideway

Binomial Theorem and Binomial Series : Output.to from Sideway

PreCalculus Binomial Theorem and Pascal's Triangle Task Ca

PreCalculus Binomial Theorem and Pascal's Triangle Task Cards and Quiz

PreCalculus Binomial Theorem and Pascal's Triangle Task Ca

The Nickzom Empire: Nickzom Solves Binomial Series Problems With Steps...

The Nickzom Empire: Nickzom Solves Binomial Series Problems With Steps...

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.

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.

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.

Binomial Theorem Task cards with HW, Quiz, Study Guides, bundled with my Binomial Theorem and Pascal's Triangle Posters (or Handouts). Great 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.

Binomial Theorem Bundle of Task Cards Quiz Posters

Binomial Theorem Task cards with HW, Quiz, Study Guides, bundled with my Binomial Theorem and Pascal's Triangle Posters (or Handouts). Great 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.

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.

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.

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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