Chứng tỏ rằng: B=\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}< 1\)
Ta có : \(B=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{8^2}\)
Mà \(\frac{1}{2^2}<\frac{1}{1.2};\frac{1}{3^2}<\frac{1}{2.3};...;\frac{1}{8^2}<\frac{1}{7.8}\)
\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{8^2}<\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{7.8}=1-\frac{1}{8}<1\)
Vậy B < 1
Ta có:\(\frac{1}{2^2}<\frac{1}{1.2};\frac{1}{3^2}<\frac{1}{2.3};......;\frac{1}{8^2}<\frac{1}{7.8}\)
<=> B<\(\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{7.8}\)
<=> B<\(\frac{1}{1}-\frac{1}{2}+.......+\frac{1}{7}-\frac{1}{8}\)
<=> B<\(1-\frac{1}{8}\)
<=> B<\(\frac{7}{8}\) <1
Chứng tỏ rằng B = \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}< 1\)
B < \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)
B < \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)
B < \(1-\frac{1}{8}\)mà 1 - 1/8 < 1
=> B < 1 ( dpcm )
Vậy ...
\(B=\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{8^2}< \frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{7.8}< 1-\frac{1}{8}=\frac{7}{8}< 1\)
Vậy B<1
Hok tốt
chứng tỏ rằng
B=\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}\)
Bài 5: Chứng tỏ rằng : B = \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}\)<1 .
chứng tỏ rằng : \(B=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}<1\)
TA CÓ B<1/1.2 +1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8
=1-1/2+1/2-1/2+1/3-1/4...+1/7-1/8
=1-1/8<1
VẬY B<1
Chứng tỏ rằng: \(B=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}<1\)
Giữ nguyên phân số 1/2^2, còn các phân số khác ta thay bằng các phân số lớn hơn, ta có:
B<1/2^2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8 = 1/4+B
Dễ dàng ta tính được:
B = 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8 = 1/2-1/8
Do đó: B<1/4+1/2-1/8<1
Chứng tỏ rằng: \(B=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}<1\)
Chứng tỏ rằng : B = \(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}<1\)
B=\(\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}\)<\(\frac{1}{2}\)
nếu có bài chứng tỏ bạn cứ bỉu là nó đã bé hơn rùi lại còn phải chứng tỏ
Ta có: B< \frac{1}{1.2} + \frac{1}{2.3} + ...+ \frac{1}{7.8}
= 1 - \frac{1}{2} + \frac{1}{2}-\frac{1}{3}+....-\frac{1}{8}
=1-\frac{1}{8}
suy ra B<1 dpcm
Chứng tỏ rằng: \(B=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}<1\)
\(B=\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+\frac{1}{8^2}<\frac{1}{1.2}+\frac{1}{2\cdot3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}=1-\frac{1}{8}=\frac{7}{8}\)
Mà \(\frac{7}{8}<1\)(đpcm)