s=1/1.2+1/3.4+1/5.6+...+1/99.100
chứng minh s<5/6
PA
Những câu hỏi liên quan
Tính : S=1.2+3.4+5.6+...+(2n-1).2n (n thuộc N*)
Tính S =1.2+3.4+5.6+...+(2n-1).2n (n thuộc N*)
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Chứng minh rằng:
a)\(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}< \frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{99.100}\)
b)\(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{99.100}< 1-\frac{1}{2.3}\)
Cần gấp, ai nhanh mik tick nha
Ai giúp đi, làm ơnnnnnnnnnnnnnnnnnnn
\(B=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(B=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{100}-2.\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{100}\right)\)
\(B=1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)\)
\(B=\frac{1}{51}+\frac{1}{52}+...+\frac{1}{100}\)
\(B< \frac{1}{60}+\frac{1}{60}+...+\frac{1}{60}\)
\(B< \frac{50}{60}\Leftrightarrow B< \frac{5}{6}\)
A=1/1.2+1/3.4+1/5.6+...+1/49.50. Chứng minh A<1
A = \(\dfrac{1}{1.2}\) + \(\dfrac{1}{3.4}\) + \(\dfrac{1}{5.6}\)+....+ \(\dfrac{1}{49.50}\)
A = \(\dfrac{1}{1}\) - \(\dfrac{1}{2}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{6}\)+ \(\dfrac{1}{49}\) - \(\dfrac{1}{50}\)
A = 1 - \(\dfrac{1}{50}\) < 1
A = \(\dfrac{1}{1.2}\) + \(\dfrac{1}{3.4}\)+.....+ \(\dfrac{1}{49.50}\) < 1 ( đpcm)
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A=1/1.2+1/3.4+1/5.6+....+1/49.50 chứng minh rằng A<1
a=1/1.2+1/3.4+1/5.6+....+1/49.50<1 chứng minh rằng a<1
Tính:
S=1.2+3.4+5.6+...+(2n-1).2n
Giups mình mai mình đi học
Ta có : S = 1.2 + 3.4 + 5.6 +.....+ (2n - 1).2n
=> 3S = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ..... + (2n - 1)2n(2n + 1)
=> 3S = (2n - 1)2n(2n + 1)
=> 3S = 2n(2n2 - 1)
=> 3S = 4n3 - 2n
=> S = \(\frac{4n^3-2n}{3}\)
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chứng minh 1/1.2+1/3.4+1/5.6+...+1/2015.2016=1/1009+1/1010+...+1/2016
Chứng minh 1/1.2 + 1/3.4 +1/5.6 +...... + 1/49.50 =1/26 + 1/27 + ... +1/50