Đáp án:
A=36/1.3.5+36/3.5.7+36/5.7.9+...+36/25.27.29
A=36/1.3.5+36/3.5.7+36/5.7.9+...+36/25.27.29
⇒A=9.(4/1.3.5+4/3.5.7+4/5.7.9+...+4/25.27.29)
⇒A=9.(4/1.3.5+4/3.5.7+4/5.7.9+...+4/25.27.29)
⇒A=9.(1/1.3−1/3.5+1/3.5−1/5.7+1/5.7−1/7.9+...+1/25.27−1/27.29)
⇒A=9.(1/1.3−1/3.5+1/3.5−1/5.7+1/5.7−1/7.9+...+1/25.27−1/27.29)
⇒A=9.(1/1.3−1/27.29)
⇒A=9.(1/3−1/783)
⇒A=9.1/3−9.1/783
⇒A=3−1/87
Vì 3−1/87<3.
⇒A<3(đpcm).
Chúc bạn học tốt <3