Cho P=50+51+52+...+52017 và Q=52018 : 4.Tính Q - P
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mk lam luon nhe!
Bot vao moi ve 3 don vi, ta co
\(\left(\frac{x-7}{50}-1\right)+\left(\frac{x-6}{51}-1\right)+\left(\frac{x-5}{52}-1\right)=\left(\frac{x-52}{5}-1\right)+\left(\frac{x-51}{6}-1\right)+\left(\frac{x-50}{7}-1\right)\)
Quy dong len ,ta co
\(\frac{x-57}{50}+\frac{x-57}{51}+\frac{x-57}{52}=\frac{x-57}{5}+\frac{x-57}{6}+\frac{x-57}{7}\)
\(\frac{x-57}{50}+\frac{x-57}{51}+\frac{x-57}{52}-\frac{x-57}{5}-\frac{x-57}{6}-\frac{x-57}{7}=0\)
(x-57).\(\left(\frac{1}{50}+\frac{1}{51}+\frac{1}{52}-\frac{1}{5}-\frac{1}{6}-\frac{1}{7}\right)=0\)
Ma \(\left(\frac{1}{50}+\frac{1}{51}+\frac{1}{52}-\frac{1}{5}-\frac{1}{6}-\frac{1}{7}\right)\) khac 0 nen => x-57=0
x=0+57 =57
Vay x =57.
Mk chac chan 100% bai nay dung
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Sửa đề: \(7^{52}+7^{51}-7^{50}\)
\(=7^{50}\left(7^2+7-1\right)=7^{50}\cdot55⋮55\)
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a.
$S=1+2+2^2+2^3+...+2^{2017}$
$2S=2+2^2+2^3+2^4+...+2^{2018}$
$\Rightarrow 2S-S=(2+2^2+2^3+2^4+...+2^{2018}) - (1+2+2^2+2^3+...+2^{2017})$
$\Rightarrow S=2^{2018}-1$
b.
$S=3+3^2+3^3+...+3^{2017}$
$3S=3^2+3^3+3^4+...+3^{2018}$
$\Rightarrow 3S-S=(3^2+3^3+3^4+...+3^{2018})-(3+3^2+3^3+...+3^{2017})$
$\Rightarrow 2S=3^{2018}-3$
$\Rightarrow S=\frac{3^{2018}-3}{2}$
Câu c, d bạn làm tương tự a,b.
c. Nhân S với 4. Kết quả: $S=\frac{4^{2018}-4}{3}$
d. Nhân S với 5. Kết quả: $S=\frac{5^{2018}-5}{4}$
5P=5+5^1+5^2+...+5^2017+5^2018
5P-1P=(5+5^2+....+5^2017+5^2018)-(5^0+5*1+...+5^2017)
4P=5^2018-1
P=(5^2018-1):4
=> Q-P=1/4
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