what is the value of

Mar 2019
318
14
iran
1/2 + 1/2×3 + 1/2×3×5 + 1/2×3×5×7 + ...
= 1/2 + 1/6 + 1/30 + 1/210 + ...
 

romsek

Math Team
Sep 2015
2,958
1,672
USA
it apparently comes out to around 0.7

Do you have some reason to suspect it has a nice closed form?
 
Aug 2012
2,488
780
1/2 + 1/2×3 + 1/2×3×5 + 1/2×3×5×7 + ...
= 1/2 + 1/6 + 1/30 + 1/210 + ...
Being a stickler for parens, I will note for the sake of any impressionable students that 1/2 x 3 = 3/2; and that the OP means 1/(2x3); and likewise for the other terms.

The rule is that multiplication and division have equal precedence; and are evaluated left to right.
 
  • Like
Reactions: 1 person