Derive an expression for the sum of the reciprocals of two consecutive odd integers

Question

Derive an expression for the sum of the reciprocals of two consecutive odd integers 2m-1 and 2m+1.

Answer 1

1/X   +    1/(X+2) =  2(x+1)/X^2 + X    (X and X+2 are any 2 con. odd #'s)

 

this is the same as:  2(X+1)/X(x+2)

 

 

Answer 2

If c is a number, then the reciprocal of that number would be 1/c.  Sum means to add.

 

[1 / (2m - 1)] + [1 / (2m + 1)]