Question

Sum((Sin((Pi*x))+1)/(-1)^x,{x,1,100})

Answer 1

Answer:

Step-by-step explanation: nπx+cosπx=0

⇒tan(πx)=−1=tan(−  

4

π

​

)

Thus general solution is,

πx=nπ−  

4

π

​

, where n∈Z

⇒x=n−  

4

1

​

 

Hence sum of solution in the given interval is

=  

k=1

∑

100

​

k−  

4

1

​

=  

2

100⋅101

​

−  

4

1

​

⋅100=5050−25=5025