- #1
SatyaDas
- 22
- 0
How to prove that for all .
Using graph, we can see that the value of this series is 1 for all values of x.
[DESMOS]{"version":7,"graph":{"viewport":{"xmin":-2.7634114187202106,"ymin":-4.543149781969371,"xmax":17.23658858127979,"ymax":8.437278166514556}},"randomSeed":"2ce535cd8c2a6f2ce21bf7669d621391","expressions":{"list":[{"type":"expression","id":"1","color":"#c74440","latex":" sum_{i=1}^{N} frac{1}{2^{3i}} left( csc^{2} left( frac{ pi x}{2^{i}} right)+1 right) sec^{2} left( frac{ pi x}{2^{i}} right) sin^{2} left( pi x right)"},{"type":"text","id":"4","text":"N substitutes for infinity. Use slider to change value."},{"type":"expression","id":"3","color":"#388c46","latex":"N=9","hidden":true,"slider":{"hardMin":true,"hardMax":true,"min":"1","max":"20","step":"1"}},{"type":"expression","id":"2","color":"#2d70b3"}]}}[/DESMOS]
Using graph, we can see that the value of this series is 1 for all values of x.
[DESMOS]{"version":7,"graph":{"viewport":{"xmin":-2.7634114187202106,"ymin":-4.543149781969371,"xmax":17.23658858127979,"ymax":8.437278166514556}},"randomSeed":"2ce535cd8c2a6f2ce21bf7669d621391","expressions":{"list":[{"type":"expression","id":"1","color":"#c74440","latex":"
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