Let a 1= 1.

Let j=i- 1

ai & gt= a(I- 1)+ 1/(2i- 1)= a(I-2)+ 1/(2i- 1)+ 1/(2i-3)

ai = 1+ 1/3+ 1/5+……+ 1/(2i- 1)

a(j+k)-aj = 1/(2j+2k- 1)+……+ 1/(2j+2- 1)>= 1/(2j+ 1)>= 1/(2j+k)= 1/(j+k+j)