P=(1/1.2+1/3.4+1/5.6+1/59.60).31.32.33...59.60 chia hết cho 91
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NT
1
ML
14 tháng 8 2015
\(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{59.60}\)
=\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{59}-\frac{1}{60}=\left(1+\frac{1}{3}+...+\frac{1}{59}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{60}\right)\)
=\(\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{59}+\frac{1}{60}\right)-2\cdot\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{60}\right)\)
=\(\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{60}\right)-\left(1+\frac{1}{2}+...+\frac{1}{30}\right)=\frac{1}{31}+\frac{1}{32}+...+\frac{1}{60}\)
O
1
S
22 tháng 4 2018
\(A=\frac{1}{1\cdot2}+\frac{1}{3\cdot4}+\frac{1}{5\cdot6}+...+\frac{1}{59\cdot60}\)
\(A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{69}-\frac{1}{60}\)
\(A=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{59}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{50}\right)\)
\(A=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{49}+\frac{1}{50}-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{50}\right)\)
\(A=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{49}+\frac{1}{50}-1-\frac{1}{2}-\frac{1}{3}-...-\frac{1}{25}\)
\(A=\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{50}\)
HM
4
DD
14 tháng 8 2016
\(\text{Có 3 trường hợp có thể xảy ra:}\)
\(A=B\)
\(A< B\)
\(A>B\)
12 tháng 7 2018
\(A=1.2+2.3+3.4+4.5+...+59.60\)
\(\Rightarrow3A=1.2.3+2.3.\left(4-1\right)+...+59.60.\left(61-58\right)\)
\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+...+59.60.61-58.59.60\)
\(\Rightarrow3A=59.60.61\)
\(\Rightarrow A=\frac{59.60.61}{3}\)
25 tháng 7 2021
\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{59.60}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{59}-\dfrac{1}{60}=1-\dfrac{1}{60}=\dfrac{59}{60}\)
25 tháng 7 2021
\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{59\cdot60}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{59}-\dfrac{1}{60}\)
\(=1-\dfrac{1}{60}=\dfrac{59}{60}\)
\(P=\left(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{59.60}\right).31.32.33....59.60\)
\(\text{Ta có:}\)
\(91=13.7\)
\(\rightarrow4.13+5.17=42.35⋮91\)
\(\left(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{59.60}\right).31.32.33....59.60\)
\(\rightarrow\left(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{59.60}\right).31.32.....60.42.35\)
\(\rightarrow\left(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{59.60}\right).31.32....60.20.91⋮91\)