Simplify i1+i2+i3+⋯+i97+i98+i99.
∑[i^n, n, 1, 99] =i - 1 - i + 1 + i - 1 - i.................... 1 + i - 1 - i = - 1. Sorry for the typo!!.
∑[i^n, n, 1, 99] =i - 1 - i + 1 + i - 1 - i + 1....................- i + 1 + i - 1 - i = - 1
i1+i2+i3+i4+i5+⋯+i97+i98+i99=(i1+i2+i3+i4)(1+i4+i8+i12+⋯+i96)−i100=(i1+i2)(1+i2)24∑k=0(i4k)−i100|i2=−1=(i1+i2)(1+i2⏟=0)24∑k=0(i4k)−i100=0−i100=−(i2)50=−(−1)50=−1