Question

Its pretty easy if you are good at math! Please help!

Answer 1

Step-by-step explanation:

Explanation:

The trick is to know about the basic idea of sequences and series and also knowing how i cycles.

The powers of i will result in either: i, −1, −i, or 1.

We can regroup i+i2+i3+⋯+i258+i259 into these categories.

We know that i=i5=i9 and so on. The same goes for the other powers of i.

So:

i+i2+i3+⋯+i258+i259

=(i+i5+⋯+i257)+(i2+i6+⋯+i258)+(i3+i7+⋯+i259)+(i4+i8+⋯+i256)

We know that within each of these groups, every term is the same, so we are just counting how much of these are repeating.

=65(i)+65(i2)+65(i3)+64(i4)

From here on out, it's pretty simple. You just evaluate the expression:

=65(i)+65(−1)+65(−i)+64(1)

=65i−65−65i+64

=−65+64

=−1

So,

i+i2+i3+⋯+i258+i259=-1