InterviewSolution
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InterviewSolution
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The value of `i^(1+3+5++(2n+1))`is, If n is odd. |
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Answer» Correct Answer - z=`{:{(,"1, if n is odd"),(,"i, if n is even"):}` Let `z = i^([1+3+5+......+(2n+1)])` Now , `1+3+5+…..+(2n+1)` are `n+1` terms of an A.P whose sum is `(n+1)/(2)[1+2n +1]=(n+1)^(2)` Hence, `z=i^((n+1))`. Now put n = 1,2,3,4,5.... `n =1,z=i^(4) = 1,n=2, z = i^(9) = i` `n=3,z=i^(16)=1,n=4` `z=i^(25)=i,n = 5,z =i^(12) = 1,......` Thus, `z{{:(,"1,if n is odd"),(,"i, if n is even"):}` |
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