Question

What is the sum `1+1/3+1/5+1/7+1/9+1/11+...` ?

Answer 1

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