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Using mathematical induction, prove that the Binomial formula holds for complex numbers (²1 Ĺ (2₁ +2₂2)" = (")424-k where where (x)=k!(n-k)! for k= 0,1,2,.... whenever 2₁, 22 € C. Hint: (₁²₁)+(1)-("+¹). =

Using mathematical induction, prove that the Binomial formula holds for complex numbers (²1 Ĺ (2₁ +2₂2)" = (")424-k where where (x)=k!(n-k)! for k= 0,1,2,.... whenever 2₁, 22 € C. Hint: (₁²₁)+(1)-("+¹). =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Using mathematical induction, prove that the Binomial formula holds for complex numbers (²₁ +22)" = k=0&212-k whenever 2₁, 22 € C. Hint: where (3) k! (n-k)! (²₁)+()-("+¹) = for k = 0,1,2,.....
Transcribed Image Text:3. Using mathematical induction, prove that the Binomial formula holds for complex numbers (²₁ +22)" = k=0&212-k whenever 2₁, 22 € C. Hint: where (3) k! (n-k)! (²₁)+()-("+¹) = for k = 0,1,2,.....
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