Page 82 - Calculus with Complex Numbers

Exam ples

Find the sum of the series

by integrating cot z(z4 round a large square contour.
Use your answer to Question 1 to lind the sums of the following series.

1 1 1
V
V
W
1+ + + +- .
Find the sum of

by integrating cosec z(z4 round a large square contour. Compare your answer
with the answer you got in Question 2.
Find the sum of
1 1 1
V
W
V
1 + + + + . . .
by integrating tan z(z4 round a large square contotm Compare with the answer
you got in Question 2.
Find the sum of
1 1 1
V
W
V
1 + + + + . . .
by integrating cot n'z/ (2z + 1)4 round a large square contotm Compare with
Questions 2 and 4.
Find the sum of
7
oo 1
) T

1 rltrl + 1)