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Q.

C1−C3+C5−C7+...

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a

2n−1

b

2n2sinnπ4

c

cosnπ4

d

0

answer is B.

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Detailed Solution

(1+i)n=C0+C1i+C2i2+…+Cnin(1-i)n=C0-C1i+C2i2+…∴(1+i)n-(1-i)n=2C1i+C3i3+C5i5+…⇒2n2cisnπ4-2n2cis-nπ4=2iC1-C3+C5-C7…⇒2n22isinnπ4=2iC1-C3+C5-…⇒C1-C3+C5-…=2n2sinnπ4
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C1−C3+C5−C7+...