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.
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.