a, 5n+1_ 4x5n+1
b, 62x64_ 43(36_ 1)
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a: Ta có: \(36\le6^x\le1296\)
\(\Leftrightarrow2\le x\le4\)
hay \(x\in\left\{2;3;4\right\}\)
b: Ta có: \(100< 5^{2x-1}< 5^6\)
\(\Leftrightarrow2x-1\in\left\{3;5\right\}\)
\(\Leftrightarrow2x\in\left\{4;6\right\}\)
hay \(x\in\left\{2;3\right\}\)
a) 2n + 29 \(⋮\) 2n + 1
\(\Rightarrow\) 2n + 29 - (2n + 1) \(⋮\) 2n + 1
\(\Rightarrow\) 28 \(⋮\) 2n + 1
\(\Rightarrow\) 2n + 1 \(\in\) Ư(28) = {1 ; 2 ; 4 ; 7 ; 14 ; 28} , mà n \(\in\) N
\(\Rightarrow\) n \(\in\) {0 ; 3}
Vậy n \(\in\) {0 ; 3}
b) 5n + 38 \(⋮\) n + 2
\(\Rightarrow\) 5n + 38 - 5(n + 2) \(⋮\) n + 2
\(\Rightarrow\) 28 \(⋮\) n + 2
\(\Rightarrow\) n + 2 \(\in\) Ư(28) = {1 ; 2 ; 4 ; 7 ; 14 ; 28}, mà n \(\in\) N
\(\Rightarrow\) n \(\in\) {0 ; 2 ; 5 ; 12 ; 26}
Vậy n \(\in\) {0 ; 2 ; 5 ; 12 ; 26}
\(b,A=\left(1+4+4^2\right)+\left(4^3+4^4+4^5\right)+...\left(4^{57}+4^{58}+4^{59}\right)\\ A=\left(1+4+4^2\right)+4^3\left(1+4+4^2\right)+...+4^{57}\left(1+4+4^2\right)\\ A=\left(1+4+4^2\right)\left(1+4^3+...+4^{57}\right)\\ A=21\left(1+4^3+...+4^{57}\right)⋮7\)
a: \(\Leftrightarrow2x+1\in\left\{1;3\right\}\)
hay \(x\in\left\{0;1\right\}\)
a: \(\Leftrightarrow2n+1\in\left\{1;3;9\right\}\)
hay \(n\in\left\{0;1;4\right\}\)
\(a,\Leftrightarrow10n+14⋮2n+1\\ \Leftrightarrow5\left(2n+1\right)+9⋮2n+1\\ \Leftrightarrow2n+1\inƯ\left(9\right)=\left\{1;3;9\right\}\\ \Leftrightarrow n\in\left\{0;1;4\right\}\)
(C=\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+\frac{13}{21}-\frac{15}{28}+\frac{17}{36}-...+\frac{197}{4851}-\frac{199}{4950})
bỏ tạm 38/25 ra
=(9/10-11/15) +(13/21-15/28) +(197/4851-199/4950)
=1/6+1/12+1/20+...+1/49*50=2450
=3-2/2x3+4-3/3x4+5-4/4x5+....50-49/49x50
=1/2-1/3+1/3-...-1/50
1/2-1/50=12/25
=38/25+12/25=50/25
=2
a, 5n+1-4.5n+1 = -3.5n+16
b,62.64-43(36-1)
= 66-26.36-26
= 66-(2.3)6-64
= 66-66-64 = -64