a) 52A=552-550+548-546+....+54-52
52A+A=(552-550+.....+54-52)+(550-548+...+52-1)
26A=552+1
A= 552+1:26
Phần c làm thế nào dzậy mọi ngừi ?????????????????????????
a: Ta có: \(A=5^{50}-5^{48}+5^{46}-5^{44}+\cdots+5^2-1\)
=>\(25A=5^{52}-5^{50}+5^{48}-5^{46}+\cdots+5^4-5^2\)
=>25A+A=\(5^{52}-5^{50}+5^{48}-5^{46}+\cdots+5^4-5^2+5^{50}-5^{48}+5^{46}-5^{44}+\cdots+5^2-1\)
=>26A=\(5^{52}-1\)
=>\(A=\frac{5^{52}-1}{26}\)
b: \(26A=5^{52}-1\)
=>\(26A+1=5^{52}\)
=>\(5^{n}=5^{52}\)
=>n=52
Bạn kiểm tra lại đề bài bị nhầm: -5^46
c) \(A=\left(5^{50}-5^{48}\right)+\left(5^{46}-5^{44}\right)+...+\left(5^6-5^4\right)+\left(5^2-1\right)\)
\(=5^{48}\left(5^2-1\right)+5^{44}\left(5^2-1\right)+...+5^4\left(5^2-1\right)+24\)
\(=5^{48}.24+5^{44}.24+...+5^2.24+24\)
\(=5^2.4\left(5^{46}.6+5^{42}.6+...+6\right)+24\)
\(=100.\left(5^{46}.6+5^{42}.6+...+6\right)+24\)chia 100 dư 24
a) Ta có :
\(A=5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4+5^2-1\)
\(\Rightarrow25A=5^{52}-5^{50}+5^{48}-5^{46}+...+5^8-5^6+5^4-5^2\)
\(\Rightarrow A+25A=5^{52}-1\)
\(\Rightarrow26A=5^{52}-1\)
\(\Rightarrow A=\frac{5^{52}-1}{26}\)
Vậy : \(A=\frac{5^{52}-1}{26}\)
b) Ta có : \(26A=5^{52}-1\)
\(\Rightarrow26A+1=5^{52}=5^n\)
\(\Rightarrow n=52\)
Vậy : \(n=52\)
b, a - b = 90 và ƯCLN(a,b) = 15
ƯCLN(a; b) = 15
a = 15k; b = 15d (k; d) =1
Theo bài ra ta có: a - b = 90
Suy ra: 15k - 15d = 90
15.(k -d) = 90
k - d = 90 : 15
k - d = 6
k = 6 + d
c, ab = 294 và ƯCLN (a,b) =7
ƯCLN(a; b) = 7
a = 7.k; b = 7.d (k; d) = 1
Theo bài ra ta có:
a.b = 7k.7d = 294
k.d = 294 : (7.7)
k.d = 6
(k; d) = (1; 6); (2; 3); (3; 2); (6; 1)
Vậy (a; b) = (7; 42); (14; 21); (21; 14); (42; 7)
a) \(A=5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4+5^2-1\)
\(5^2\cdot A=5^2\cdot\left(5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4+5^2-1\right)\)
\(\Rightarrow25A=5^{52}-5^{50}+5^{48}-5^{46}+...+5^8-5^6+5^4-5^2\)
\(\Rightarrow25A+A=\left(5^{52}-5^{50}+5^{48}-5^{46}+...+5^8-5^6+5^4-5^2\right)\)
\(+\left(5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4+5^2-1\right)\)
\(\Rightarrow26A=5^{52}-1\)
\(\Rightarrow A=\frac{5^{52}-1}{26}\)
b) Ta có: \(26\cdot A+1=5^n\)
\(\Rightarrow26\cdot\frac{5^{52}-1}{26}+1=5^n\)
\(\Rightarrow5^{52}-1+1=5^n\)
\(\Rightarrow5^{52}=5^n\Rightarrow n=52\)
c)
Tận cùng của tất cả các số ngoại trừ 1 có tận cùng là 25
-> (25-25)+(25-25)+(25-25)+...+(25-25)+(25-1)=24
-> A có tận cùng là 24->A:100 dư 24
. h mk nhé
a) �=550−548+546−544+...+56−54+52−1A=550−548+546−544+...+56−54+52−1
52⋅�=52⋅(550−548+546−544+...+56−54+52−1)52⋅A=52⋅(550−548+546−544+...+56−54+52−1)
⇒25�=552−550+548−546+...+58−56+54−52⇒25A=552−550+548−546+...+58−5
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