Ta thấy: 7 + 7² + 7³ + 7⁴ = 7 + 49 + 343 + 2401 = 2800 chia hết cho 20²

P = 7 + 7² + 7³ + ... + 7²⁰¹⁶ = ( 7 + 7² + 7³ + 7⁴) + 7⁴( 7 + 7² + 7³ + 7⁴) + ... +  7²⁰¹²( 7 + 7² + 7³ + 7⁴)

P = 2800 + 7⁴ . 2800 + ... + 7²⁰¹² . 2800 = 2800( 1 + 7⁴ + ... + 7²⁰¹² )

Mà 2800 chia hết cho 20² \(⇒\)  P chia hết cho 20² 

uk chán quá

Buồn quá

a)Ta có: \(VT=7^6+7^5-7^4\)

\(=7^4\left(7^2+7-1\right)=7^4\cdot55⋮55\)

Vậy \(7^6+7^5-7^4⋮55\)

b)\(A=1+5+...+5^{100}\)

\(5A=5\left(1+5+...+5^{100}\right)\)

\(5A=5+5^2+...+5^{101}\)

\(5A-A=\left(5+5^2+...+5^{101}\right)-\left(1+5+...+5^{100}\right)\)

\(4A=5^{101}-1\Rightarrow A=\frac{5^{101}-1}{4}\)

1 \(-\)\(\frac{1}{3.5}\)\(-\)\(\frac{1}{5.7}\)\(-\)\(\frac{1}{7.9}\)\(-\)..... \(-\)\(\frac{1}{53.55}\)\(-\)\(\frac{1}{55.57}\)

= 1 \(-\)( \(\frac{1}{3.5}\)  + \(\frac{1}{5.7}\) + \(\frac{1}{7.9}\) + ..... + \(\frac{1}{53.55}\)  + \(\frac{1}{55.57}\)  )

= 1 \(-\)( \(\frac{1}{3}\)\(-\)\(\frac{1}{5}\)+ \(\frac{1}{5}\)\(-\)\(\frac{1}{7}\)+ \(\frac{1}{7}\)\(-\)\(\frac{1}{9}\)+....+ \(\frac{1}{53}\)\(-\)\(\frac{1}{55}\)+ \(\frac{1}{55}\)\(-\)\(\frac{1}{57}\)) . \(\frac{1}{2}\)

= 1 \(-\)( \(\frac{1}{3}\)\(-\)\(\frac{1}{57}\)) . \(\frac{1}{2}\)

= 1 \(-\) \(\frac{6}{19}\). \(\frac{1}{2}\)= 1 \(-\)\(\frac{3}{19}\)= \(\frac{16}{19}\)

\(1-\frac{1}{3.5}-\frac{1}{5.7}-\frac{1}{7.9}-...-\frac{1}{53.55}-\frac{1}{55.57}\)

đặt \(A=1-\frac{1}{3.5}-\frac{1}{5.7}-\frac{1}{7.9}-...-\frac{1}{53.55}-\frac{1}{55.57}\)

\(A=1-\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{53.55}+\frac{1}{55.57}\right)\)

đặt \(B=\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+.....+\frac{1}{53.55}+\frac{1}{55.57}\)

\(2B=2\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{53.55}+\frac{1}{55.57}\right)\)

\(2B=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{53.55}+\frac{2}{55.57}\)

\(2B=\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+....+\frac{55-53}{53.55}+\frac{57-55}{55.57}\)

\(2B=\frac{5}{3.5}-\frac{3}{3.5}+\frac{7}{5.7}-\frac{5}{5.7}+\frac{9}{7.9}-\frac{7}{7.9}+...+\frac{55}{53.55}-\frac{53}{53.55}+\frac{57}{55.57}-\frac{55}{55.57}\)

\(2B=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{53}-\frac{1}{55}+\frac{1}{55}-\frac{1}{57}\)

\(2B=\frac{1}{3}-\frac{1}{57}\)

\(2B=\frac{54}{171}\)

\(\Rightarrow B=\frac{54}{171}:2\)

\(\Rightarrow B=\frac{9}{57}\)

mà \(A=1-B\)

\(\Rightarrow A=1-\frac{9}{57}\)

\(\Rightarrow A=\frac{48}{57}\)

chúc bạn học giỏi ^^

\(\sqrt{x+2}\ge0\left(voimoix\right)=>\sqrt{x+2}+\frac{3}{11}\ge\frac{3}{11}\left(voimoix\right)\)

=>\(B_{max}=\frac{3}{11}\)

dấu "=" xảy ra

<=>x=0

vậy.....

Vì: x - y + 2x = -30

=> \(\frac{x+1-y+2+2z}{3-4+2.5}=\frac{-30+3}{9}=-\frac{27}{9}=-3\)

=> x = -3 . 3 - 1 = -10

y = -3 . 4 + 2 = -10

z = -3 . 5 = -15 

còn lời giải thì đợi chút 

Văn hay Toán zợ ?

?????????