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from manimlib.imports import *
import numpy as np
class convergence(Scene):
def construct(self):
originalFormula=TextMobject("$\sum _{ n=0 }^{ \infty }{ { a }_{ n }{ x }^{ n } }$")
originalFormula.set_color(RED)
self.play(Write(originalFormula))
self.wait(1)
self.play(ApplyMethod(originalFormula.shift,2.7*UP))
self.wait(1)
terms=["$a_{ 0 }$","$a_{ 1 }x$","$a_{ 2 }x^{ 2 }$","$a_{ 3 }x^{ 3 }$","$a_{ 4 }x^{ 4 }$","$a_{ 5 }x^{ 5 }$","$a_{ 6 }x^{ 6 }$","$a_{ 7 }x^{ 7 }$","$a_{ 8 }x^{ 8 }$","$a_{ 9 }x^{ 9 }$","$a_{ 10 }x^{ 10 }$","$a_{ 11 }x^{ 11 }$"]
termsTogetherString="+".join(terms)
termsTogether=TextMobject(termsTogetherString+"...")
termsTogether.scale(0.8)
termsTogether.shift(2.7*UP)
self.play(ReplacementTransform(originalFormula,termsTogether))
self.wait(1)
termMobjectRect=[0]*12
termMobject=TextMobject(terms[0])
termMobject.shift(2.7*UP+6.2*LEFT)
for i in range(1,13):
termMobjectOld=termMobject
termMobjectOld.scale(0.8)
if(i<12):
termMobject=TextMobject(terms[i])
termMobject.next_to(termMobjectOld)
if(i==1):
rectDefine=TextMobject("Here","each rectangle","represents the","value of the term")
rectDefine.set_color_by_tex_to_color_map({"each rectangle":BLUE,"value of the term":YELLOW})
rectDefine.scale(0.7)
rectDefine.shift(3.2*DOWN)
self.play(Write(rectDefine))
self.wait(1)
if(i==2):
ratio=TextMobject("If $\\frac { a_{ n+1 } }{ { a }_{ n } } < 1$")
ratio.set_color(RED)
ratio.scale(0.7)
ratio.move_to(3.2*DOWN)
inequality=TextMobject("$a_{ n+1 } < a_{ n }$")
inequality.set_color(RED)
inequality.scale(0.7)
inequality.move_to(3.2*DOWN)
self.play(FadeOut(rectDefine))
self.play(Write(ratio))
self.wait(1)
self.play(ReplacementTransform(ratio,inequality))
self.wait(1)
#self.play(ApplyMethod(termMobjectOld.move_to,(2-0.3*i)*DOWN+RIGHT*0.2*i))
termMobjectRect[i-1]=Rectangle(height=0.1,width=(5-0.4*i))
termMobjectRect[i-1].move_to((2-0.2*i)*DOWN+RIGHT*0.2*i)
#rectangles[p] = termMobjectRect
#p+=1
self.play(ReplacementTransform(termMobjectOld,termMobjectRect[i-1]))
uparrow=TextMobject("$\\uparrow$")
uparrow.set_color(GREEN)
uparrow.scale(6)
uparrow.shift(4*RIGHT+0.5*DOWN)
self.play(ShowCreation(uparrow))
self.wait(1)
converges=TextMobject("Converges!")
converges.set_color(RED)
converges.scale(0.6)
converges.next_to(uparrow)
self.play(FadeIn(converges))
self.wait(2)
self.play(FadeOut(converges),FadeOut(uparrow),FadeOut(inequality))
self.wait(0.5)
rect=VGroup(termMobjectRect[0],termMobjectRect[1],termMobjectRect[2],termMobjectRect[3],termMobjectRect[4],termMobjectRect[5],termMobjectRect[6],termMobjectRect[7],termMobjectRect[8],termMobjectRect[9],termMobjectRect[10],termMobjectRect[11])
self.play(ApplyMethod(rect.scale,0.2))
for i in range(0,12):
self.play(ApplyMethod(termMobjectRect[i].shift,i*0.04*DOWN+(11-(3-0.11*i)*i)*LEFT*0.3))
func=TextMobject("$\\approx$","$f(x)$")
func.set_color_by_tex_to_color_map({"$f(x)$":RED})
func.scale(0.8)
func.shift(DOWN+4.5*RIGHT+0.1*UP)
self.play(FadeIn(func))
rightarrow=TextMobject("$\\rightarrow$")
rightarrow.set_color(GREEN)
rightarrow.scale(4)
rightarrow.shift(2*DOWN)
converges=TextMobject("Hence even the","sum converges!")
converges.set_color_by_tex_to_color_map({"sum converges!":RED})
converges.move_to(3*DOWN)
converges.scale(0.7)
self.play(Write(rightarrow),FadeIn(converges))
self.wait(2)
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