The value ofi - i2 - i3 - i4 - - - i100 equal is

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The value ofi...

Question

The value of $i - i^{2} + i^{3} - i^{4} + \dots - i^{100}$ equal is

$i$

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$- i$

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$0$

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$1 + i$

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Solution

The correct option is C
$0$

The explanation for the correct answer.
Solve for the value of given series.
The given series $i - i^{2} + i^{3} - i^{4} + \dots - i^{100}$
Here, the first term $a = i$
Common ratio, $r = - i$
Sum of $n$ terms of GP
$= a \times \frac{(1 - r^{n})}{(1 - r)}$
$= i \times \frac{(1 - {(- i)}^{100})}{(1 + i)} = i \times \frac{(1 - {(- 1)}^{100} {(i)}^{100})}{(1 + i)} = i \times 0 = 0$
Hence, option C is correct .

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is equal to

Q. Given that

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and

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.
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The value ofi–i2+i3–i4+…–i100 equal is

The value of $i - i^{2} + i^{3} - i^{4} + \dots - i^{100}$ equal is