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from manimlib.imports import *
class divergence(GraphScene):
CONFIG = {
"y_max" : 2,
"y_min" : -2,
"x_max" : 20,
"x_min" : 0,
"y_tick_frequency" : 1,
"x_tick_frequency" : 1,
"axes_color" : WHITE,
"num_graph_anchor_points": 3000,
"graph_origin" : ORIGIN+6*LEFT,
"x_labeled_nums": None,
"y_labeled_nums": [-2,-1,1,2],
"x_axis_label":r"${(-1)}^{n}$",
"y_axis_label":"$Sum$",
"x_axis_width": 10,
"y_axis_height": 4,
}
def construct(self):
XTD = self.x_axis_width/(self.x_max - self.x_min)
YTD = self.y_axis_height/(self.y_max - self.y_min)
text1 = TextMobject("Consider the series 1-1+1-1+1-1+1-......")
self.add(text1)
self.wait(3)
self.play(FadeOut(text1))
self.setup_axes()
rangeo = (20)//self.x_axis_width
for i in range(0,2):
texta = TextMobject(str((-1)**i)).move_to(self.graph_origin+0.2*(rangeo*i)*RIGHT+0.5*DOWN+0.5*RIGHT)
self.add(texta)
for i in range(2,4):
texta = TextMobject(str((-1)**i)).move_to(self.graph_origin+0.2*(rangeo*i)*RIGHT+0.5*DOWN+0.65*RIGHT)
self.add(texta)
for i in range(4,6):
texta = TextMobject(str((-1)**i)).move_to(self.graph_origin+0.2*(rangeo*i)*RIGHT+0.5*DOWN+0.8*RIGHT)
self.add(texta)
for i in range(6,8):
texta = TextMobject(str((-1)**i)).move_to(self.graph_origin+0.2*(rangeo*i)*RIGHT+0.5*DOWN+0.95*RIGHT)
self.add(texta)
for i in range(8,10):
texta = TextMobject(str((-1)**i)).move_to(self.graph_origin+0.2*(rangeo*i)*RIGHT+0.5*DOWN+1.1*RIGHT)
self.add(texta)
for i in range(10,12):
texta = TextMobject(str((-1)**i)).move_to(self.graph_origin+0.2*(rangeo*i)*RIGHT+0.5*DOWN+1.35*RIGHT)
self.add(texta)
for i in range(12,14):
texta = TextMobject(str((-1)**i)).move_to(self.graph_origin+0.2*(rangeo*i)*RIGHT+0.5*DOWN+1.5*RIGHT)
self.add(texta)
for i in range(14,16):
texta = TextMobject(str((-1)**i)).move_to(self.graph_origin+0.2*(rangeo*i)*RIGHT+0.5*DOWN+1.65*RIGHT)
self.add(texta)
for i in range(16,18):
texta = TextMobject(str((-1)**i)).move_to(self.graph_origin+0.2*(rangeo*i)*RIGHT+0.5*DOWN+1.8*RIGHT)
self.add(texta)
for i in range(18,20):
texta = TextMobject(str((-1)**i)).move_to(self.graph_origin+0.2*(rangeo*i)*RIGHT+0.5*DOWN+1.95*RIGHT)
self.add(texta)
text2 = TextMobject("Number of purple lines denotes the number of terms added").move_to(1*UP).scale(0.8)
self.play(ShowCreation(text2))
self.wait(4)
self.play(FadeOut(text2))
for i in range(0,2):
horline = Line(np.array([-5.5+i,1,0]), np.array([-5+i,1,0]), color = PINK)
verline = DashedVMobject(Line(np.array([-5+i,1,0]), np.array([-5+i,0,0])))
botline = Line(np.array([-6+i,0,0]), np.array([-5.5+i,0,0]), color = PINK)
upline = DashedVMobject(Line(np.array([-5.5+i,0,0]), np.array([-5.5+i,1,0])))
self.play(ShowCreation(botline), run_time = 0.2)
self.play(ShowCreation(upline), run_time = 0.2)
self.play(ShowCreation(horline), run_time = 0.2)
self.play(ShowCreation(verline), run_time = 0.2)
text3 = TextMobject("For even number of terms, sum is 0").move_to(1*UP).scale(0.8)
self.play(FadeIn(text3))
self.wait(4)
self.play(FadeOut(text3))
for i in range(2,4):
horline = Line(np.array([-5.5+i,1,0]), np.array([-5+i,1,0]), color = PINK)
verline = DashedVMobject(Line(np.array([-5+i,1,0]), np.array([-5+i,0,0])))
botline = Line(np.array([-6+i,0,0]), np.array([-5.5+i,0,0]), color = PINK)
upline = DashedVMobject(Line(np.array([-5.5+i,0,0]), np.array([-5.5+i,1,0])))
self.play(ShowCreation(botline), run_time = 0.2)
self.play(ShowCreation(upline), run_time = 0.2)
self.play(ShowCreation(horline), run_time = 0.2)
self.play(ShowCreation(verline), run_time = 0.2)
botline = Line(np.array([-6+4,0,0]), np.array([-5.5+4,0,0]), color = PINK)
upline = DashedVMobject(Line(np.array([-5.5+4,0,0]), np.array([-5.5+4,1,0])))
self.play(ShowCreation(botline))
self.play(ShowCreation(upline))
text4 = TextMobject("For odd number of terms, sum is 1").move_to(1.5*UP).scale(0.8)
self.play(FadeIn(text4))
self.wait(3)
for i in range(4,10):
horline = Line(np.array([-5.5+i,1,0]), np.array([-5+i,1,0]), color = PINK)
verline = DashedVMobject(Line(np.array([-5+i,1,0]), np.array([-5+i,0,0])))
botline = Line(np.array([-6+i,0,0]), np.array([-5.5+i,0,0]), color = PINK)
upline = DashedVMobject(Line(np.array([-5.5+i,0,0]), np.array([-5.5+i,1,0])))
self.play(ShowCreation(botline), run_time = 0.2)
self.play(ShowCreation(upline), run_time = 0.2)
self.play(ShowCreation(horline), run_time = 0.2)
self.play(ShowCreation(verline), run_time = 0.2)
text5 = TextMobject("The sum is oscillating between 1 and 0").move_to(1.5*UP).scale(0.8)
self.play(ReplacementTransform(text4, text5))
self.wait(4)
text6 = TextMobject("It does not coerce to a particular finite value").move_to(1.5*UP).scale(0.8)
self.play(ReplacementTransform(text5, text6))
self.wait(4)
text7 = TextMobject("Hence it diverges").move_to(1.5*UP).scale(0.8)
self.play(ReplacementTransform(text6, text7))
self.wait(3)
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