Chứng minh rằng a)2/3×5+2/5×7+2/7×9+…+2/97×99>32% b) 1/21+1/22+…+1/40>7/12 AI ĐÚNG MK TICK ĐÚNG BẰNG 2 NICK 21/10/2021 Bởi Raelynn Chứng minh rằng a)2/3×5+2/5×7+2/7×9+…+2/97×99>32% b) 1/21+1/22+…+1/40>7/12 AI ĐÚNG MK TICK ĐÚNG BẰNG 2 NICK
a)2/3×5+2/5×7+…+2/97×99 =1/3-1/5+1/5-1/7+…+1/97-1/99 =1/3-1/99 =32/99 Mà 32/99>32%=>2/3×5+2/5×7+…+2/97×99>32% b)1/21+1/22+…+1/40>7/12 Ta có 1/21<1/30;1/22>1/30;…;1/29>1/30 =>1/21+1/22+…+1/30>1/30+…+1/30=1/3 (1) 1/31>1/40;1/32>1/40;…;1/39>1/40 =>1/31+1/32+…+1/39+1/40>1/40+…+1/40=1/4 (2) Từ (1) và (2)=>1/21+1/22+…+1/30+1/31+1/32+…+1/39+1/40>1/3+1/4 =>1/21+1/22+…+1/40>7/12 Bình luận
a)2/3×5+2/5×7+…+2/97×99
=1/3-1/5+1/5-1/7+…+1/97-1/99
=1/3-1/99
=32/99
Mà 32/99>32%=>2/3×5+2/5×7+…+2/97×99>32%
b)1/21+1/22+…+1/40>7/12
Ta có 1/21<1/30;1/22>1/30;…;1/29>1/30
=>1/21+1/22+…+1/30>1/30+…+1/30=1/3 (1)
1/31>1/40;1/32>1/40;…;1/39>1/40
=>1/31+1/32+…+1/39+1/40>1/40+…+1/40=1/4 (2)
Từ (1) và (2)=>1/21+1/22+…+1/30+1/31+1/32+…+1/39+1/40>1/3+1/4
=>1/21+1/22+…+1/40>7/12