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  4. If i2=-1, then the sum i+i2+i3+... upto 1000 terms is equal to:

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Q. If $ {{i}^{2}}=-1, $ then the sum $ i+{{i}^{2}}+{{i}^{3}}+... $ upto 1000 terms is equal to:

KEAMKEAM 2002

Solution:

$ i+{{i}^{2}}+{{i}^{3}}+... $ upto 1000 terms $ =\frac{i(1-{{i}^{1000}})}{1-i}=\frac{i(1-1)}{1-i} $ $ =\frac{i}{1-i}\times 0=0 $