Cho M = 1/15+1/105+1/315+.............+1/9177. So sánh M với 1/2
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Cho M=1/15+1/105+1/315+...+1/9177
So sánh M với 1/12
Cho M= 1/15 + 1/105 + 1/315+....+1/9177. So sanh M vs 12.
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S=1/1.3.5 +1/3.5.7+...................+1/19.21.23
---> 4S=4/1.3.5 + 4/ 3.5.7 +.........................+4/19.21.23
= (1/1.3 -1/3.5 ) + ( 1/3.5 -1/3.7) +...................................+(1/... -1/21.23 )
= 1/1.3 -1/21.23
= 1/3 -1/483 =160/483
----> S = 160/483 : 4 = 160 / 1932
(em tự rút gọn nhé! )S=1/1.3.5 +1/3.5.7+...................+1/19.21.23
---> 4S=4/1.3.5 + 4/ 3.5.7 +.........................+4/19.21.23
= (1/1.3 -1/3.5 ) + ( 1/3.5 -1/3.7) +...................................+(1/... -1/21.23 )
= 1/1.3 -1/21.23
= 1/3 -1/483 =160/483
----> S = 160/483 : 4 = 160 / 1932
(em tự rút gọn nhé! )
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M=1/1.3.5 +1/3.5.7+.....+1/19.21.23
4M=4/1.3.5 + 4/ 3.5.7 +...+4/19.21.23
= (1/1.3 -1/3.5 ) + ( 1/3.5 -1/3.7) +....+(1/19.21 -1/21.23 )
= 1/1.3 -1/21.23
= 1/3 -1/483
=160/483
⇒ S = 160/483 : 4
= 160 / 1932
=40/438
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1) Cho M=\(\frac{1}{15}\)+\(\frac{1}{105}\)+\(\frac{1}{315}\)+...+\(\frac{1}{9177}\)
So sánh M với \(\frac{1}{12}\)
cho M = \(\frac{1}{15}+\frac{1}{105}+\frac{1}{315}+....+\frac{1}{9177}\). so sánh M với \(\frac{1}{12}\)
\(M=\frac{1}{15}+\frac{1}{105}+\frac{1}{315}+...+\frac{1}{9177}\)
\(M=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{19.21.23}\)
\(M=\frac{1}{4}\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{19.21}-\frac{1}{21.23}\right)\)
\(M=\frac{1}{4}\left(\frac{1}{1.3}-\frac{1}{21.23}\right)< \frac{1}{4}.\frac{1}{1.3}=\frac{1}{12}\)
\(\Rightarrow M< \frac{1}{12}\)
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M=\(\frac{1}{15}\)+\(\frac{1}{105}\)+\(\frac{1}{315}\)+...+\(\frac{1}{9177}\)
So sánh M với \(\frac{1}{12}\)
\(\text{M}< \frac{1}{12}\)
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Xem thêm câu trả lời
Cho M= 1/5 +1/105 +1/315+...+1/9177. So sanh M vs 12
cho M= 1/15 + 1/105 + 1/315+...+ 1/1977. So sanh M vs 12.
cho M= 1/15 + 1/105 + 1/315+...+ 1/1977. So sanh M vs 12.
cho M= 1/15 + 1/105 + 1/315+...+ 1/1977. So sanh M vs 12.