What is the sum #1+1/3+1/5+1/7+1/9+1/11+...# ?
1 Answer
Nov 27, 2017
Like the harmonic series, this sum does not converge.
Explanation:
This sum does not converge.
#1+color(red)(1/3)+color(orange)(1/5+1/7)+color(green)(1/9+1/11+1/13+1/15)+color(purple)(1/17+1/19+1/21+1/23+1/25+1/27+1/29+1/31)+color(blue)(1/33+)... #
#> 1+color(red)(1/4)+color(orange)(1/8+1/8)+color(green)(1/16+1/16+1/16+1/16)+color(purple)(1/32+1/32+1/32+1/32+1/32+1/32+1/32+1/32)+color(blue)(1/64+)...#
#= 1+color(red)(1/4)+color(orange)(1/4)+color(green)(1/4)+color(purple)(1/4)+...#
does not converge
