Question 150163
Set up a table of values for k and the argument, {{{(-2)^k}}}.
EXCEL is a great program to do this.
{{{k=1}}},{{{ -2^k=-2^1=-2}}}
{{{k=2}}},{{{ -2^k=-2^2=4}}}
{{{k=3}}},{{{ -2^k=-2^3=-8}}}
{{{k=4}}},{{{ -2^k=-2^4=16}}}
{{{k=5}}},{{{ -2^k=-2^5=-32}}}
{{{k=6}}},{{{ -2^k=-2^6=64}}}
{{{k=7}}},{{{ -2^k=-2^7=-128}}}
{{{k=8}}},{{{ -2^k=-2^8=256}}}
{{{k=9}}},{{{ -2^k=-2^9=-512}}}
{{{k=10}}},{{{ -2^k=-2^10=1024}}}
Sum the first ten terms,
{{{-2+4-8+16-32+64-128+256-512+1024=682}}}
{{{sum( (-2)^k, 1, 10 )=682}}}