S=5+52+53+...+52006 CM S chia het cho 126
S=5+52+53+...+52006
a,tính S
b,c/m s⋮126
a) \(S=5+5^2+...+5^{2006}\)
\(5S=5^2+5^3+...+5^{2007}\)
\(5S-S=5^2+5^3+5^4+...+5^{2007}-5-5^2-5^3-...-5^{2006}\)
\(4S=5^{2007}-5\)
\(S=\dfrac{5^{2007}-5}{4}\)
b) \(S=5+5^2+5^3+...+5^{2006}\)
\(S=\left(5+5^4\right)+\left(5^2+5^5\right)+...+\left(5^{2003}+5^{2006}\right)\)
\(S=5\cdot\left(1+5^3\right)+5^2\cdot\left(1+5^3\right)+...+5^{2003}\cdot\left(1+5^3\right)\)
\(S=\left(1+5^3\right)\cdot\left(5+5^2+...+5^{2003}\right)\)
\(S=126\cdot\left(5+5^2+...+5^{2003}\right)\) ⋮ 126
S = 5 + 52 + 53 + .....+ 596 . Chứng minh : S \(⋮\) 126 .
S=(5+52+53+54+55+56)+...+(591+592+593+594+595+596)S=(5+52+53+54+55+56)+...+(591+592+593+594+595+596)
=5(1+5+52+53+54+55)+...+591(1+52+53+54+55)=5.3906+...+591.3906=3906(5+...+596)=3.126(5+...+591)=5(1+5+52+53+54+55)+...+591(1+52+53+54+55)=5.3906+...+591.3906=3906(5+...+596)=3.126(5+...+591)
chia hết cho 126
cho S =5+52+53+54+55+56+...+52012
chứng tỏ S chia hết cho 65
S = 5 + 5² + 5³ + 5⁴ + ... + 5²⁰¹²
= (5 + 5² + 5³ + 5⁴) + (5⁵ + 5⁶ + 5⁷ + 5⁸) + ... + (5²⁰⁰⁹ + 5²⁰¹⁰ + 5²⁰¹¹ + 5²⁰¹²)
= 780 + 5⁴.(5 + 5² + 5³ + 5⁴) + ... + 5²⁰⁰⁸.(5 + 5² + 5³ + 5⁴)
= 780 + 5⁴.780 + ... + 5²⁰⁰⁸.780
= 65.12 + 5⁴.65.12 + ... + 5²⁰⁰⁸.65.12
= 65.12(1 + 5⁴ + ... + 5²⁰⁰⁸) ⋮ 65
Vậy S ⋮ 65
\(S=5\left(1+5+5^2+5^3\right)+5^5\left(1+5+5^2+5^3\right)+...+5^{2009}\left(1+5+5^2+5^3\right)\)
\(=156\left(5+5^5+...+5^{2009}\right)\)
\(=780\cdot\left(1+5^4+...+5^{2008}\right)⋮65\)
cho S= 5+5^2+5^3...+5^2006
a, tinh S
b,Chung minh rang S chia het cho 126
Cho S = 5+5^2+5^3+5^4+5^5+5^6+..+5^2004. Chứng minh S chia het cho 126 va 65
Câu hỏi của Phương Thảo Trần - Toán lớp 0 | Học trực tuyến
cho S=5+52+53+..........+52006
a,Tinh S
b,Chung minh S chia het cho 126
S = 5 + 52 + 53 + ......... + 52006
5S = 52 + 53 + 54 + .......... + 52007
5S - S = ( 52 + 53 + 54 + .......... + 52007) - ( 5 + 52 + 53 + ......... + 52006 )
4S = 52007 - 5
S = \(\frac{5^{2007}-5}{4}\)
a)\(S=5+5^2+5^3+.....+5^{2006}\Rightarrow5S=5^2+5^3+5^4+\)\(....+5^{2007}\)
\(\Rightarrow5S-S=\left(5^2+5^3+5^4+....+5^{2007}\right)-\left(5+5^2+5^3+.....+5^{2006}\right)\)
\(\Rightarrow4S=5^{2007}-5\Rightarrow S=\frac{5^{2007}-5}{4}\)
\(a.S=5+5^2+5^3+......+5^{2006}\)
\(S=\left(5+5^2+5^3+5^4+5^5+5^6\right)+.....+\left(5^{2001}+5^{2002}+.....+5^{2006}\right)\)
\(S=5.\left(1+5+5^2+5^3+5^4+5^5\right)+......+5^{2001}\left(1+5+5^2+5^3+5^4+5^5\right)\)
\(S=5.3906+........+5^{2001}.3906\)
\(S=3906\left(5+....+5^{2001}\right)\)
\(b.S=3906\left(5+....+5^{2001}\right)\)
\(S=126.3\left(5+....+5^{2001}\right)\)
\(\Rightarrow\text{S chia hết cho 126}\)
S = 5^2 + 5^3 + 5^4 + ... + 5^2006 chia het cho 126
S = 5 + 52 + 53 +....+52006
S= (5+52+53+54+55+56) +.....+ ( 22001+52002+52003+52004+52005+52006)
S= 5 x ( 1+5+52+53+5455 ) +......+ 52001x (1+5+5 2+53+54+55)
S= 5 x 3906+.........+ 52001 x 3906
S = 3906x( 5+..+52001)
S = 3906 x ( 5+...+52001)
S = 126 x 3 x ( 5+...+52001)
=> S chia hết 126
Cho S = 1 - 5 + 52 - 53 +.... + 598 - 599
a)Tính S b)CMR: 5100 chia cho 6 dư 1
0\(a.S=1-5+5^2-5^3+...+5^{98}-5^{99}\\ 5S=5-5^2+5^3-5^4+.....+5^{99}-5^{100}\\ 5S+S=\left(5-5^2+5^3-5^4+.....+5^{99}-5^{100}\right)+\left(1-5^{ }+5^2-5^3+.....+5^{98}-5^{99}\right)\\ 6S=1-5^{100}\\ S=\dfrac{1-5^{100}}{6}\\ \)
\(b,S6=1-5^{100}\\ 1-S6=5^{100}\)
=> 5100 chia 6 du 1
e đang cần gấp, có ai đến giúp e ko?
\(S=1-5+5^2-5^3+...+5^{98}-5^{99}\\ a,S=5^0.\left(1-5\right)+5^2.\left(1-5\right)+...+5^{98}.\left(1-5\right)=-4.\left(5^0+5^2+5^4+...+5^{98}\right)\)
cho S = 5 + 52 + 53 + 54 + 55 + 56 +...+ 52016. chứng tỏ rằng S chia hết cho 65
mn giúp mk nhé!!