Câu hỏi của Võ Ngọc Phương

Question

Tính:

$A=\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+...+\dfrac{1}{44.49}\right).\dfrac{1-3-5-7-...-49}{89}$

Giải chi tiết dùm mik nha. Thankss

Nguyễn Minh Dương · Accepted Answer

$A=\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+..+\dfrac{1}{44.49}\right)\left(\dfrac{1-3-5-7-..-49}{89}\right)\ A=\dfrac{1}{5}\left(\dfrac{5}{4.9}+\dfrac{5}{9.14}+..+\dfrac{5}{44.49}\right)\left(\dfrac{1-3-5-7-...-49}{89}\right)\ A=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{49}\right)\left(\dfrac{1-3-5-7-...-49}{89}\right)$

$A=\dfrac{9}{196}\left(\dfrac{1-3-5-7-...-49}{89}\right)$

Ta đặt: $P=1-3-5-7-...-49\
=1-\left(3+5+7+..+49\right)\
=1-624\
=-623\
\Rightarrow\dfrac{9}{196}.-\dfrac{623}{89}=-\dfrac{9}{28}.$Câu trả lời: $A=\left(\dfrac{1}{4.9}+\dfrac{1}{9.14}+..+\dfrac{1}{44.49}\right)\left(\dfrac{1-3-5-7-..-49}{89}\right)\ A=\dfrac{1}{5}\left(\dfrac{5}{4.9}+\dfrac{5}{9.14}+..+\dfrac{5}{44.49}\right)\left(\dfrac{1-3-5-7-...-49}{89}\right)\ A=\dfrac{1}{5}\left(\dfrac{1}{4}-\dfrac{1}{49}\right)\left(\dfrac{1-3-5-7-...-49}{89}\right)$

$A=\dfrac{9}{196}\left(\dfrac{1-3-5-7-...-49}{89}\right)$

Ta đặt: $P=1-3-5-7-...-49\
=1-\left(3+5+7+..+49\right)\
=1-624\
=-623\
\Rightarrow\dfrac{9}{196}.-\dfrac{623}{89}=-\dfrac{9}{28}.$

Nguyễn Nhân Dương · Answer

Ta có: �=(14⋅9+19⋅14+114⋅19+...+144⋅49)⋅1−3−5−7−...−4989A=(4⋅91​+9⋅141​+14⋅191​+...+44⋅491​)⋅891−3−5−7−...−49​

⇔�=15⋅(54⋅9+59⋅14+514⋅19+...+544⋅49)⋅1−3−5−7−...−4989⇔A=51​⋅(4⋅95​+9⋅145​+14⋅195​+...+44⋅495​)⋅891−3−5−7−...−49​

⇔�=15⋅(14−19+19−114+114−119+...+144−149)⋅1−3−5−7−...−4989⇔A=51​⋅(41​−91​+91​−141​+141​−191​+...+441​−491​)⋅891−3−5−7−...−49​

⇔�=15⋅(14−149)⋅1−3−5−7−...−4989⇔A=51​⋅(41​−491​)⋅891−3−5−7−...−49​

⇔�=15⋅(49−44⋅49)⋅1−3−5−7−...−4989⇔A=51​⋅(4⋅4949−4​)⋅891−3−5−7−...−49​

⇔�=15⋅45196⋅1−3−5−7−...−4989⇔A=51​⋅19645​⋅891−3−5−7−...−49​

⇔�=9196⋅1−3−5−7−...−4989⇔A=1969​⋅891−3−5−7−...−49​

⇔�=9196⋅−62389=−928⇔A=1969​⋅89−623​=−289​
 Câu trả lời: Ta có: �=(14⋅9+19⋅14+114⋅19+...+144⋅49)⋅1−3−5−7−...−4989A=(4⋅91​+9⋅141​+14⋅191​+...+44⋅491​)⋅891−3−5−7−...−49​

⇔�=15⋅(54⋅9+59⋅14+514⋅19+...+544⋅49)⋅1−3−5−7−...−4989⇔A=51​⋅(4⋅95​+9⋅145​+14⋅195​+...+44⋅495​)⋅891−3−5−7−...−49​

⇔�=15⋅(14−19+19−114+114−119+...+144−149)⋅1−3−5−7−...−4989⇔A=51​⋅(41​−91​+91​−141​+141​−191​+...+441​−491​)⋅891−3−5−7−...−49​

⇔�=15⋅(14−149)⋅1−3−5−7−...−4989⇔A=51​⋅(41​−491​)⋅891−3−5−7−...−49​

⇔�=15⋅(49−44⋅49)⋅1−3−5−7−...−4989⇔A=51​⋅(4⋅4949−4​)⋅891−3−5−7−...−49​

⇔�=15⋅45196⋅1−3−5−7−...−4989⇔A=51​⋅19645​⋅891−3−5−7−...−49​

⇔�=9196⋅1−3−5−7−...−4989⇔A=1969​⋅891−3−5−7−...−49​

⇔�=9196⋅−62389=−928⇔A=1969​⋅89−623​=−289​

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