Channel: Think Twice

Category: Education

Tags: mind blowthink twiceeducationmathematicsmathsnumberssumbestalgebravideoexplainedsummationnumberhowphysicsofn squaredproofintuitionvisual math equationsmaths tricksodd numbersconsecutive odd integersnumberphilemath problems3d animationvisual mathematicsvisual mathmaticsoddsimple explanationvisual math learningvisual math problemsarithmetic seriesseriessum of first odd numbers3b1bgeometricmath tricksmath videosgeometrymath

Description: Short animation about the sum of first n odd numbers. here is an algebraic proof: The first n odd natural numbers are 1, 3, 5, ... 2n-1. This forms an arithmetic progression with first term 1, common difference 2 and last term (2n-1). The sum is given by S = 1+3+5+...+(2n-1). Using S = n (First term + Last term)/2, we get S = n (1+2n-1)/2, which simplifies to S = n^2. Subscribe for more:) _________________________________________________________________ Support my animations on: patreon.com/Think_twice _________________________________________________________________ Any further questions or ideas: Email - thinktwiceask@gmail.com Twitter - twitter.com/thinktwice2580 _________________________________________________________________ Overall render time: ~ 8 hours Programs used: - Cinema 4D (3D animation) _________________________________________________________________ Music: CLAUDE DEBUSSY: CLAIR DE LUNE