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Grade 9Magical Mathematics[Interesting Approach]

Calculate the value of C3+C7+C11......

Leo Pixie

12 Years agoGrade 9

1 Answer

Arun Kumar

12 Years ago

Hello Student,

We know that

$\\(1+x)^n \\=>C_1+C_3+C_5....=2^{n-1} \\$on putting x=i and equating real and imaginary parts$ \\C_1-C_3+C_5-C_7....=2^{n-1}sin{\n\pi \over 4} \\$subtracting we get $ \\ C_3+C_7+C_{11}....={2^{n-1}-2^{n-1}sin{\n\pi \over 4} \over 2}$

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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