Evaluate: $(- 1)^{1} + (- 1)^{2} + . . . . . + (- 1)^{98} + (- 1)^{99}$

- 1

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Solution

The correct option is A $- 1$
$(- 1)^{2 n} = 1$
$(- 1)^{2 n - 1} = - 1$

Using this principle,

$(- 1)^{1} + (- 1)^{2} = - 1 + 1 = 0$
$(- 1)^{3} + (- 1)^{4} = - 1 + 1 = 0$
.
.
.
.
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$(- 1)^{97} + (- 1)^{98} = 0$
$(- 1)^{99} = - 1$

Sum is $0 + 0 + 0..... + 0 + - 1 = - 1$

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Evaluate: (−1)1+(−1)2+.....+(−1)98+(−1)99

The correct option is A −1(−1)2n=1(−1)2n−1=−1Using this principle,(−1)1+(−1)2=−1+1=0(−1)3+(−1)4=−1+1=0.....(−1)97+(−1)98=0(−1)99=−1Sum is 0+0+0.....+0+−1=−1

Evaluate: $(- 1)^{1} + (- 1)^{2} + . . . . . + (- 1)^{98} + (- 1)^{99}$

The correct option is A $- 1$
$(- 1)^{2 n} = 1$
$(- 1)^{2 n - 1} = - 1$

Using this principle,

$(- 1)^{1} + (- 1)^{2} = - 1 + 1 = 0$
$(- 1)^{3} + (- 1)^{4} = - 1 + 1 = 0$
.
.
.
.
.
$(- 1)^{97} + (- 1)^{98} = 0$
$(- 1)^{99} = - 1$

Sum is $0 + 0 + 0..... + 0 + - 1 = - 1$