#(-1)^{-10} + (-1)^{-9} + (-1)^{-8} + \cdots + (-1)^9 + (-1)^{10}# (The dots #\cdots# mean that there are 21 numbers being added, one for each integer from #-10# to 10.) ?

1 Answer
Hriman
Jul 23, 2018

The sum of the sequence is #1#

Explanation:

Logically, if we are adding #1# and #-1# repeatedly, the sum is #0#, but since the first and last terms of the sequence are both #1# , we know that in the sequence there is one more #1# than #-1#.

We can prove it with a geometric sum formula for finite sums:
#S_n= a_1((1-r^n)/(1-r))#

#S_21= 1((1-(-1)^(21))/(1-(-1)))#

#S_21= 1(2/2)#

#S_21= 1#

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