Cho A= 1-5+9-13+17-21+... Biết A= 2021. Hỏi A có bao nhiêu số hạng? Giá trị của số hạng cuối là bao nhiêu?
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a. \(x^2+y^2+z^2=xy+yz+xz\)
\(\Leftrightarrow x^2+y^2+z^2-xy-yz-xz=0\)
\(\Leftrightarrow2x^2+2y^2+2z^2-2xy-2yz-2zx=0\)
\(\Leftrightarrow\left(x-y\right)^2+\left(y-z\right)^2+\left(z-x\right)^2=0\)
Vì \(\hept{\begin{cases}\left(x-y\right)^2\ge0\\\left(y-z\right)^2\ge0\\\left(z-x\right)^2\ge0\end{cases}}\Leftrightarrow\hept{\begin{cases}x-y=0\\y-z=0\\z-x=0\end{cases}}\Leftrightarrow x=y=z\)( đpcm )

She has never known a more warmed-heart than her mother has.
=> Her mother has the most warm-hearted person She has ever known.

320 : ( x - 1 ) = ( 53 - 52 ) : 4 + 15
<=> 320 : ( x - 1 ) = ( 125 - 25 ) : 4 + 15
<=> 320 : ( x - 1 ) = 100 : 4 + 15
<=> 320 : ( x - 1 ) = 40
<=> x - 1 = 8
<=> x = 9
240 : ( x - 5 ) = 22 . 52 - 20
<=> 240 : ( x - 5 ) = 4 . 25 - 20
<=> 240 : ( x - 5 ) = 80
<=> x - 5 = 3
<=> x = 8
70 : ( x - 3 ) = ( 34 - 1 ) : 4 - 16
<=> 70 : ( x - 3 ) = 80 : 4 - 16
<=> 70 : ( x - 3 ) = 4
<=> x - 3 = 35/2
<=> x = 41/2
a) 320: (x-1) = (53 - 52):4 + 15 b) 240: (x-5) = 22.52 - 20 c) 70:(x-3) = (34 - 1):4 - 16
320: (x-1) = (125- 25): 4 + 15 240: (x-5) = 4.25 - 20 70:(x-3) = (81-1): 4 - 16
320: (x-1) = 100:4 + 15 240: (x-5) = 100 - 20 70: (x-3) = 80: 4 - 16
320: (x-1) = 25 + 15 240: (x-5) = 80 70: (x-3) = 20 -16
320: (x-1) = 40 (x-5) = 240:80 70: (x-3) = 4
(x-1) = 320:40 (x-5) = 3 (x-3) = 70:4
(x-1) = 80 x = 5+3 (x-3) = 17,5
x = 80+1 x = 8 x = 17,5 : 3
x = 81 x = 5,83

This is the first time we' ve gone to Da Nang
=> We have never gone to Da Nang
STUDY WELL ^^__^^

I have known her for a long time
=> I began known her for a long time
STUDY WELL ^^__^^

This is the first time his sister has bought a cheaper shirt than this one.

1 cặp có giá trị là:
\(\frac{1}{11}\)+\(\frac{1}{25}\)=\(\frac{36}{275}\)
Có các phân số là;
(25-11):1+1=15(phân số)
Có các cặp là :
15 :2=7(CẶP ,DƯ 1 CẶP)
1 CẶP DƯ ĐÓ LÀ:
\(\frac{36}{275}\):2=\(\frac{36}{550}\)=\(\frac{18}{275}\)
Các cặp có tổng là:
\(\frac{36}{275}\).7=\(\frac{252}{275}\)
Tổng số đó là:
\(\frac{252}{275}\)+\(\frac{18}{275}\)=\(\frac{270}{275}\)=\(\frac{54}{55}\)
Phân số \(\frac{54}{55}\)lớn hơn phân số \(\frac{47}{60}\)vì
\(\frac{54}{55}\)và \(\frac{47}{60}\)=\(\frac{3240}{3300}\)và \(\frac{2585}{3300}\)
\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+...+\frac{1}{25}\)
\(=\left(\frac{1}{11}+\frac{1}{12}\right)+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}\right)+\left(\frac{1}{21}+\frac{1}{22}+\frac{1}{23}+\frac{1}{24}+\frac{1}{25}\right)\)
\(\frac{1}{11}+\frac{1}{12}>\frac{1}{12}+\frac{1}{12}=\frac{2}{12}=\frac{10}{60}\)
\(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}>\frac{1}{15}+\frac{1}{15}+\frac{1}{15}=\frac{3}{15}=\frac{12}{60}\)
\(\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+\frac{1}{20}=\frac{5}{20}=\frac{15}{60}\)
\(\frac{1}{21}+\frac{1}{22}+\frac{1}{23}+\frac{1}{24}+\frac{1}{25}>\frac{1}{25}+\frac{1}{25}+\frac{1}{25}+\frac{1}{25}+\frac{1}{25}=\frac{5}{25}=\frac{1}{5}=\frac{12}{60}\)
\(\Rightarrow\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+...+\frac{1}{25}>\frac{10}{60}+\frac{12}{60}+\frac{15}{60}+\frac{12}{60}=\frac{49}{60}\)
Mà \(\frac{49}{60}>\frac{47}{60}\)
\(\Rightarrow\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+...+\frac{1}{25}>\frac{47}{60}\left(đpcm\right)\)
bạn nào biết trả lời nhanh giúp mik nha