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D= 1/1 - 1 /2 + 1/2 - 1/4 + 1/4 - 1/7 +...+ 1/46 - 1/56
D= 1/1 - 1/56
D= 55/56
vậy D= 55/56
P=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{46}-\frac{1}{56}\)
P=\(1-\frac{1}{56}\)
P=\(\frac{55}{56}\)
\(P=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{46}-\frac{1}{56}\)
\(P=1-\frac{1}{56}\)
\(P=\frac{55}{56}\)
P= 1/1 -1/2 + 1/2 -1/4 + 1/4 - 1/7 +....+ 1/46 -1/56
P= 1/1 - 1/56
=> P= 55/ 56
\(S=\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{49.50}\)
\(S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{49}-\frac{1}{50}\)
\(S=\frac{1}{1}-\frac{1}{50}=\frac{49}{50}\)
\(T=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{40.43}+\frac{3}{43.46}\)
\(T=\frac{4-1}{1.4}+\frac{7-4}{4.7}+\frac{10-7}{7.10}+....+\frac{43-40}{40.43}+\frac{46-43}{43.46}\)
\(T=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{40}-\frac{1}{43}+\frac{1}{43}-\frac{1}{46}\)
\(T=\frac{1}{1}-\frac{1}{46}=\frac{45}{46}\)
1) Ta có : \(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{99.100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
Vậy T = \(=\frac{99}{100}\)
2) Ta có : \(T=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+.....+\frac{3}{43.46}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+....+\frac{1}{43}-\frac{1}{46}\)
\(=1-\frac{1}{46}=\frac{45}{46}\)
Vậy T = \(\frac{45}{46}\)
Bg
a)\(\frac{1^2}{1.2}.\frac{2^2}{2.3}.\frac{3^2}{3.4}.....\frac{99^2}{99.100}.\frac{100^2}{100.101}\)
\(=\frac{1^2.2^2.3^2.....99^2.100^2}{1.2.2.3.3.4.....99.100.100.101}\)
\(=\frac{1^2}{101}\)
\(=\frac{1}{101}\)
Ghi chú: \(=\frac{1^2.2^2.3^2.....99^2.100^2}{1.2.2.3.3.4.....99.100.100.101}\)--> 22 chịt tiêu 2.2 (trên và dưới) làm thế này mãi đến khi còn \(\frac{1^2}{101}\).
b) \(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}.....\frac{59^2}{58.60}\)
=\(\frac{2^2.3^2.4^2.....59^2}{1.3.2.4.3.5.....58.60}\)
= \(\frac{2}{1}.\frac{59}{60}\)
= \(\frac{59}{30}\)
Ghi chú: \(\frac{2^2.3^2.4^2.....59^2}{1.3.2.4.3.5.....58.60}\)--> chịt tiêu liên tục, còn \(\frac{2}{1}.\frac{59}{60}\).
P=1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{4}\)+...........+\(\frac{1}{46}\)-\(\frac{1}{56}\)
P=1-\(\frac{1}{56}\)
P=\(\frac{55}{56}\)
p=55/56