Question

If1-1/3+1/5-1/7+1/9-1/11+.........=180/4,then value of 1/1.3+1/5.7+1/9.11+.....is

Answer 1

S=1/3+1/15+1/35+1/63+1/99+1/143+1/195

S=1/1.3+1/3.5+1/5.7+1/7.9+1/9.11+1/11.13+1/13.15.

S=1/2.[(1/1–1/3)+(1/3–1/5)+(1/5–1/7)+(1/7–1/9)+(1/9–1/11)+(1/11–1/13)+(1/13–1/15)].

S=1/2.[1/1–1/15].

S=1/2.(14/15)

S=7/15. Answer.