tinh tong:
M=(-4/1*5)-(4/5*9)-(4/n-4)*n
a) 5/6 x 11/4 - 5/4 x 23/6
b) 9/16 x 13/4 - 9/4 x 5/16 + 9/16 x 17/
hay tinh tong:
1/1 x 2 + 1/2 x 3 + 1/3 x 4 + .... + 1/n (n + 1)
chung minh:
1/22 + 1/32 + 1/42 + ..... + 1/n2 < 1
giai dum nhe
biiet n!=1*2*3*4........................n;
tinh 1*1!2*2!3*3!4*4!5*5!
1!=1
2!=2
3!=6
4!=24
5!=120
1*1!*2*2!*3*3#*4*4!*5*5! = 5!*2!*3!*4!*5! = 120*2*6*24*120 = 4147200
biet n! =1*2**3*...*n . tinh 1*1!+2*2!+3*3!+4*4!+5*5!=?
Có trong Violympic Toán vòng 3 đó đáp án là 719 nha !!!
tinh
a,1+2+3+4+...+n
b,2+4+6+8+...+2n
c1+3+5+7+...+(2n+1)
d,1+5+9+...+2005
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!
Cho S=-4/1 . 4/5 - 4/5 . 4/9 - 4/9 . 4/13 - ........- 4/2013 . 4/2017
Tinh 2017S
1+1+1+2+2+2+3+3+3+4+4+4+5+5+5+6+6+6+7+7+7+8+8+8+9+9+9+.......+n
Tìm n
Phải có kết quả thì mới tìm n được chứ
1+1+1+2+2+2+3+3+3+4+4+4+5+5+5+6+6+6+7+7+7+8+8+8+9+9+9+.......+n
=3x(1+2+3..+n)
=3x(2+1).n/2
=3(n+1)n/2
Tinh nhanh:
m)5^1+5^2+5^3+...+5^199+5^200
n)3^0-3^2+3^3-3^4+...+3^2017-3^2018+3^2019-3^2020
o)6+6*9+6*9^2+6*9^3+...+6*9^99
p)(-1)*(-1^2)*(-1^3)*(-1^4)*...*(-1^99)*-(1^100)
Giup minh nhe!
Đặt \(A=5+5^2+5^3+....+5^{199}+5^{200}\)
\(\Leftrightarrow5A=5\left(5+5^2+5^3+....+5^{199}+5^{200}\right)\)
\(\Leftrightarrow5A=5^2+5^3+5^4+....+5^{200}+5^{201}\)
\(\Leftrightarrow5A-A=\left(5^2+5^3+5^4+....+5^{200}+5^{201}\right)-\left(5+5^2+5^3+....+5^{199}+5^{200}\right)\)
\(\Leftrightarrow4A=5^{201}-5\)
\(\Leftrightarrow A=\frac{5^{201}-5}{4}\)
B = 1 + 5 + 52 + 53 + ....... + 52008 + 52009
S = 1 + 2 + 5 + 14 + ....... + 3n-1 + 1/2 (với n thuộc Z)
A = 1 + 3/2^3 + 4/2^4 + 5/2^5 + ...... + 100/2^100
Q = 1 + 1/2*(1+2) + 1/3*(1+2+3) + 1/4*(1+2+3+4) + ...... + 1/20*(1+2+3+.....+20)
M = -4/1*5 - 4/5*9 - 4/9*13 - ....... - 4/(n+4)*n
Giúp mk với! Mk đang cần gấp lắm !!!!!
\(B=1+5+5^2+5^3+...+5^{2008}+5^{2009}\)
\(\Rightarrow 5B=5+5^2+5^3+5^4+...+5^{2009}+5^{2010}\)
Trừ theo vế:
\(5B-B=(5+5^2+5^3+5^4+...+5^{2009}+5^{2010})-(1+5+5^2+...+5^{2009})\)
\(4B=5^{2010}-1\)
\(B=\frac{5^{2010}-1}{4}\)
\(S=\frac{3^0+1}{2}+\frac{3^1+1}{2}+\frac{3^2+1}{2}+..+\frac{3^{n-1}+1}{2}\)
\(=\frac{3^0+3^1+3^2+...+3^{n-1}}{2}+\frac{\underbrace{1+1+...+1}_{n}}{2}\)
\(=\frac{3^0+3^1+3^2+..+3^{n-1}}{2}+\frac{n}{2}\)
Đặt \(X=3^0+3^1+3^2+..+3^{n-1}\)
\(\Rightarrow 3X=3^1+3^2+3^3+...+3^{n}\)
Trừ theo vế:
\(3X-X=3^n-3^0=3^n-1\)
\(\Rightarrow X=\frac{3^n-1}{2}\). Do đó \(S=\frac{3^n-1}{4}+\frac{n}{2}\)
\(A=1+\frac{3}{2^3}+\frac{4}{2^4}+\frac{5}{2^5}+...+\frac{100}{2^{100}}\)
\(\Rightarrow 2A=2+\frac{3}{2^2}+\frac{4}{2^3}+\frac{5}{2^4}+...+\frac{100}{2^{99}}\)
Trừ theo vế:
\(2A-A=1+\frac{3}{2^2}+\frac{4-3}{2^3}+\frac{5-4}{2^4}+\frac{6-5}{2^5}+...+\frac{100-99}{2^{99}}-\frac{100}{2^{100}}\)
\(\Leftrightarrow A=1+\frac{3}{4}-\frac{100}{2^{100}}+(\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{99}})\)
Đặt \(T=(\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{99}})\)
\(\Rightarrow 2T=\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{98}}\)
Trừ theo vế: \(2T-T=\frac{1}{2^2}-\frac{1}{2^{99}}\)
\(\Leftrightarrow T=\frac{1}{4}-\frac{1}{2^{99}}\)
Do đó: \(A=1+\frac{3}{4}-\frac{100}{2^{100}}+\frac{1}{4}-\frac{1}{2^{99}}=2-\frac{102}{2^{100}}\)