2*2^2+3*2^3+4*2^4+5*2^5+...+n*2^n=2^n+10
TQ
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tim x thuoc N bieta, 125.n 5 7b, 2 3.n 3 4 2 5 5c, 2 3 2 n 3 2.n.5 10 10 2d, 5 n=
125
Tính toán
1) S 1+2+3+4+...+n
2) S 1*2*3...*n
3)S 2+4+6+...+n
4)S 1+3+5+...+n
5)S 2*4*6...*n
6)S 1-2+3-4+...+n
7)S -1+2-3+4+...+n
8)S 1+4+9+16+...+n*n
9)S 1+9+25+...+( n mod 2 1)^2
10)S 4+16+...+( n mod 2 0)^2
11)S 5+10+15+...+ n mod 5 0
12)S 1+2-3+4+5-6+7+8-9...+n-(n mod 3 0 )
13)S 1+2!+3!+4!...+n!
14)S 1+(1+2)+(1+2+3)+...+( tổng các số từ 1 tới )( i chạy từ 1 tới n)
15)S 1*2+2*3+4*5+...+(n-1)*n
HELP ME!
Đọc tiếp
Tính toán
1) S = 1+2+3+4+...+n
2) S = 1*2*3...*n
3)S = 2+4+6+...+n
4)S = 1+3+5+...+n
5)S = 2*4*6...*n
6)S = 1-2+3-4+...+n
7)S = -1+2-3+4+...+n
8)S = 1+4+9+16+...+n*n
9)S = 1+9+25+...+( n mod 2 = 1)^2
10)S =4+16+...+( n mod 2 = 0)^2
11)S =5+10+15+...+ n mod 5 =0
12)S = 1+2-3+4+5-6+7+8-9...+n-(n mod 3 = 0 )
13)S = 1+2!+3!+4!...+n!
14)S =1+(1+2)+(1+2+3)+...+( tổng các số từ 1 tới )( i chạy từ 1 tới n)
15)S =1*2+2*3+4*5+...+(n-1)*n
HELP ME!
Tính tổng đại số
\(A=\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}-\dfrac{1}{5}-\dfrac{2}{5}-\dfrac{3}{5}-\dfrac{4}{5}+...+\dfrac{1}{10}+\dfrac{2}{10}+...+\dfrac{9}{10}\)
\(B=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}+...+\dfrac{1}{n}+\dfrac{2}{n}+...+\dfrac{n-1}{n}\)\(\left(n\in Z,n\ge2\right)\)
Tìm n biết
2x2^2+3×2^3+4×2^4+5×2^5+...+n×2^n=2^n+10
1, Thực hiện phép tính bằng cách hợp lý:
A=(1)/(2)-(2)/(5)+(1)/(3)+(5)/(7)-(-1)/(6)+(-4)/(35)+(1)/(41)
2, Chứng minh rằng:
a, 1+4+4^2+4^3+...+4^99 chia hết cho 5
b, 3^n+2-2^n+2+3^n-2^n chia hết cho 10 (với n thuộc N*)
1. \(A=\frac{1}{2}-\frac{2}{5}+\frac{1}{3}+\frac{5}{7}-\frac{-1}{6}+\frac{-4}{35}+\frac{1}{41}\)
\(=\frac{1}{2}-\frac{2}{5}+\frac{1}{3}+\frac{5}{7}+\frac{1}{6}-\frac{4}{35}+\frac{1}{41}\)
\(=\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}\right)-\left(\frac{2}{5}-\frac{5}{7}+\frac{4}{35}\right)+\frac{1}{41}\)
\(=\left(\frac{5}{6}+\frac{1}{6}\right)-\left(\frac{-11}{35}+\frac{4}{35}\right)+\frac{1}{41}\)\(=1-\frac{-7}{35}+\frac{1}{41}=1+\frac{1}{5}+\frac{1}{41}=\frac{251}{205}\)
2. a) \(1+4+4^2+4^3+......+4^{99}=\left(1+4\right)+\left(4^2+4^3\right)+.......+\left(4^{98}+4^{99}\right)\)
\(=\left(1+4\right)+4^2\left(1+4\right)+.........+4^{98}\left(1+4\right)\)
\(=5+4^2.5+........+4^{98}.5=5\left(1+4^2+.....+4^{98}\right)⋮5\)( đpcm )
b) \(3^{n+2}-2^{n+2}+3^n-2^n=\left(3^{n+2}+3^n\right)-\left(2^{n+2}+2^n\right)\)
\(=3^n\left(3^2+1\right)-2^n\left(2^2+1\right)=3^n\left(9+1\right)-2^n\left(4+1\right)\)
\(=3^n.10-2^n.5=3^n.10-2^{n-1+1}.5=3^n.10-2^{n-1}.2.5\)
\(=3^n.10-2^{n-1}.10=10\left(3^n-2^{n-1}\right)⋮10\)( đpcm )
1. Tìm a,b,c biết:a) a/b 8/5; b/c 2/7 và a+b+c 61b) ab 1/2; bc 2/3; ac 3/4c) 3a2b; 5b 7c và 3a + 5c - 7b 602. tìm các số nguyên n sao cho:1) 5^n + 5^n+2 6502) 32^-n .16^n 10243) 3^-1 .3^n+ 5. 3^n-1 1624) 125. 5ge5^nge5 . 255) (n^54)^2 n6) 243ge3^nge9.277) 2^n+3 . 2^n 1448)33^nle2349) 8. 16ge2^nge410) 4^15. 9^152^n.3^n 18^16. 2^1611) 4^11. 25^11le2^n. 5^nle20^12. 5^1212)frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5} 2^n13) 9. 27^n 3^514) (2^3 : 4) . 2^n 415)...
Đọc tiếp
1. Tìm a,b,c biết:
a) a/b = 8/5; b/c = 2/7 và a+b+c= 61
b) ab = 1/2; bc= 2/3; ac = 3/4
c) 3a=2b; 5b = 7c và 3a + 5c - 7b= 60
2. tìm các số nguyên n sao cho:
1) 5^n + 5^n+2 = 650
2) 32^-n .16^n = 1024
3) 3^-1 .3^n+ 5. 3^n-1 = 162
4) 125. 5\(\ge\)5^n\(\ge\)5 . 25
5) (n^54)^2 = n
6) 243\(\ge\)3^n\(\ge\)9.27
7) 2^n+3 . 2^n = 144
8)3<3^n\(\le\)234
9) 8. 16\(\ge\)2^n\(\ge\)4
10) 4^15. 9^15<2^n.3^n< 18^16. 2^16
11) 4^11. 25^11\(\le\)2^n. 5^n\(\le\)20^12. 5^12
12)\(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\).\(\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}\)= 2^n
13) 9. 27^n= 3^5
14) (2^3 : 4) . 2^n= 4
15) 3^-2 . 3^4. 3^n = 3^7
16)2^-1. 2^n +4.2^n=9.2^5
tim x thuoc N biet
a, 125.n=5^7
b, 2^3.n-3^4=2^5-5
c, (2^3+2) n+3^2.n.5-10=10^2
d, 5^n.5=125
e, 9 be hon hoac bang 3^n<90
f, (3n+1)^3=64
tim x thuoc N biet
a, 125.n=5^7
b, 2^3.n-3^4=2^5-5
c, (2^3+2) n+3^2.n.5-10=10^2
d, 5^n.5=125
e, 9 be hon hoac bang 3^n<90
f, (3n+1)^3=64
tim x thuoc N biet
a, 125.n=5^7
b, 2^3.n-3^4=2^5-5
c, (2^3+2) n+3^2.n.5-10=10^2
d, 5^n.5=125
e, 9 be hon hoac bang 3^n<90
f, (3n+1)^3=64
a: =>n*5^3=5^7
=>n=5^4=625
c: \(\Leftrightarrow2\cdot3^n=3^4+2^5-5=81+32-5=108\)
=>3^n=54
=>\(n\in\varnothing\)
d: =>5^n=25
=>n=2
f: =>3n+1=4
=>3n=3
=>n=1
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