Understanding Engineering Mathematics

7. (i) π−

8

π

∑∞

n= 1

cos( 2 n− 1 )t

( 2 n− 1 )^2

(ii) 2

∑∞

n= 1

(− 1 )n

n

sinnt

(iii)

π^2

3

+ 4

∑∞

n= 1

(− 1 )n

n^2

cosnt

(iv)

π

4

+

1

π

∑∞

n= 1

((− 1 )n− 1 )

n^2

cosnt+

∑∞

n= 1

(− 1 )n

n

sinnt

(v)

∑∞

n= 1

[

4

πn^2

((− 1 )n− 1 )−

2 π

n

(− 1 )n

]

sinnt

(vi)

1

2

+

∑∞

n= 1

( 1 −(− 1 )n)

nπ

sinnt

(vii)

π

2

+

1

8

+

∑∞

n= 1

3

2 nπ

sin

(nπ

2

)

cosnt+

∑∞

n= 1

1

2 nπ

(

cosnπ−cos

(nπ

2

))

sinnt