i-2 -3i+4 .........to 100 terms =?

Answers (1)

Solution:    We have   ,     S=i+2i^2+3i^3+.........+100i^100    .......(1)

                  Rightarrow                     iS= hspace0.4cmi^2+2i^3+.........+99i^100+100i^101    ........(2)

                  From   (1)-(2)    

                 Rightarrow                  (1-i)S=[i+i^2+i^3+........100 hspace0.2cmterm]-100i^101

                 Rightarrow                   S(1-i)=fraci(1-i^100)1-i-100(i^2)^50cdot i

                 Rightarrow                S=-frac1001-i=50(1-i).

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