Question

the value of the following ,where i= sqrt(-1).

Answer 1

\[\sqrt{-1} = i\] it's and imaginary number

Answer 2

\[\sum_{n=1}^{13}(i^n+i^{n+1})=?\]

Answer 3

@Sjano my question is above stated

Answer 4

try spiting up the summation in to two summations over the addition, then use the geometric formula for the two sums.

Answer 5

which geometric form..

Answer 6

if you have:\[\sum_{k=1}^nr^k=\frac{r^{n+1}-r}{r-1}\]i believe that should do the job.

Answer 7

should i do the summation fully upto 13 or i can get it by only common sense

Answer 8

(sqrt-1-1)+(-1-sqrt-1)+(-sqrt-1+1)+(1+sqrt-1)+(sqrt-1-1)+(-1-sqrt-1)+(-sqrt-1+1)+(1+sqrt-1)+(sqrt-1-1)+(-1-sqrt-1)+(-sqrt-1+1)+(1+sqrt-1)+(sqrt-1-1)
=sqrt-1-1

Answer 9

I have done the same thing but isn't there a short trick. I mean i don't want to sum it fully.

Answer 10

k thanx! i got it