A=1+2+3+4+...+2016+2017
B=1x2+2x3+3x4+...+2017x2018
C=1x2x3+2x3x4+3x4x5+...+n x (n+1)x(n+2)
D=3333...3 x 6666...6 ( Chú thích: 3333...3 có 100 chữ số 3 ; 6666...6 có 100 chữ số 6)
Bạn nào làm đúng và có lời giải thì mình tk cho nhé!
C=1x2+2x3+3x4+........+99x100
D=1x2x3+2x3x4+3x4x5+.......+98x99x100
E=12+22+52+.......+992
F=1/1x2+1/2x3+..........+1/99x100
G=1/1x2x3+1/2x3x4+........+1/99x98x100
H= 1/1x2x3x4+1/3x4x5x6+............+1/97x98x99x100
K= 1+1/2(1+2)+1/3(1+2+3)+........+1/30(1+2+30)
L=1/21+1/22+1/23+1/24+..............+1/210
M=2015/2015x2017-20162
\(\frac{ }{ }\)
sao nhiều vậy!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
F = 1- 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100
= 1 - 1/100
= 99/100
Tính :
a) 1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+.....+1
b)1/1x2x3+1/2x3x4+1/3x4x5+.....+1/98x99x100
bạn li-ke cho I love U thì ai giải cho bạn nữa
Tính :
a) 1/1x2+1/2x3+1/3x4+1/4x5+1/5x6+.....+1
b)1/1x2x3+1/2x3x4+1/3x4x5+.....+1/98x99x100
A = 1x2 +2x3+3x4+........+99 x 100
B = 1x2x3 + 2x3x4 + 4x5x6 +...........+ 98 x99 x 100
tính A,B
A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3
A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)
A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.
A x 3 = 99x100x101
A = 99x100x101 : 3
A = 333300
Ta có:
\(A=1.2+2.3+3.4+...+99.100\)
\(\Rightarrow3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)\)
\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)
\(\Leftrightarrow3A=99.100.101\Leftrightarrow A=\frac{99.100.101}{3}=333300\)
\(B=1.2.3+2.3.4+4.5.6+...+98.99.100\)
\(\Rightarrow4B=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)+4.5.6.\left(7-3\right)+...+98.99.100.\left(101-97\right)\)
\(\Rightarrow4B=1.2.3.4+2.3.4.5-1.2.3.4+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100\)
\(\Leftrightarrow4B=98.99.100.101\Leftrightarrow B=\frac{98.99.100.101}{4}=24497550\)
A= 1 x 2 + 2 x 3 + 3 x 4 +........+ 99 x 100
=> 2 + 6 + 12 +........+ 9900
=> 8 + 12 +.....+ 9900
=> 20 +....+ 9900
=> 20 + 20 + 30 +....+ 9900
=> 70 +....+ 9900
=> ( 9900 x 70 ) : 2
=> 693000 : 2
=> 346500
B = 1 x 2 x 3 + 2 x 3 x 4 +......+ 98 x 99 x100
=> ( 1 x 2 x 3) + ( 2 x 3 x 4 ) +....+ ( 98 x 99 x 100 )
= 6 + 24 +.......+ 970200
=> 28 + 120 +...+ 970200
=> ( 148 x 970200 ) : 2
=> 143589600 : 2
=> 71794900
A=1x2+2x3+3x4+...+49x50
B=1x3+3x5+5x7+...+99x101
C=1x2x3+2x3x4+3x4x5+...+50x51x52
D=1x4+2x5+3x6+...+60x63
E=1x1+2x2+3x3+...+50x50
F=1x1+3x3+5x5+...+71x71
G=1x1+4x4+7x7+...+100x100
I=1x2x3+3x4x5+5x6x7+...+69x70x71
A=1x2+2x3+3x4+...+49x50
3A= 3(1.2+2.3+3.4+...+49.50)
3A= 1.2.3+2.3.3+3.4.3+...+49.50.3
3A= 1.2.(3-0)+2.3(4-1)+3.4(5-2)+...+49.50.(51-48)
3A= 0.1.2-1.2.3+1.2.3-2.3.4+2.3.4-3.4.5+...+48.49.50-49.50.51
3A= 49.50.51
A= 49.50.51/3=41650
B=1x3+3x5+5x7+...+99x101
B=1/1.3 +1/3.5 +...+1/99.101
2B=2/1.3 + 2/3.5 +...+2/99.101
2B=1-1/3+1/3-1/5+...+1/99-1/101
2B=1-1/101
2B=100/101
B=100/101:2=100/202
C=1x2x3+2x3x4+3x4x5+...+50x51x52
Nhân C với 4 ta được:
C x 4 = 1x2x3x4 + 2x3x4x 4 + 3x4x5x4 +…+50x51x52x4
C x 4 = 1x2x3x4 + 2x3x4x(5-1) + 3x4x5x(6-2) + ... + 50x51x52x(53-49)
C x 4 = 1x2x3x4 + 2x3x4x5 - 1x2x3x4 + 3x4x5x6 - 2x3x4x5 + ... +49x 50x51x52 - 50x51x52x53
Sau khi cộng - trừ giản ước ta có : C x 4 = 50x51x52x53
C = 50x51x52x53 : 4 = 1756950
1, a, Tính (2 cách)
A=1x2+2x3+3x4+....+nx(n+1)
b, Nêu cách tính tổng quát
c, áp dụng tính
B=1x2x3+2x3x4+....+(n-1)x(n+1)
giúp mình với đang cần gấp
a)
\(A=1.2+2.3+3.4+...+n.\left(n+1\right)\)
\(3A=1.2.3+2.3.3+3.4.3+...+n.\left(n+1\right).3\)
\(3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+n.\left(n+1\right).\left[\left(n+2\right)-\left(n-1\right)\right]\)
\(3A=(1.2.3-0.1.2)+\left(2.3.4-1.2.3\right)+\left(3.4.5-2.3.5\right)+...+\left[n.\left(n+1\right).\left(n+2\right)-\left(n-1\right).n.\left(n+1\right)\right]\)\(3A=-0.1.2+n.\left(n+1\right).\left(n+2\right)\)
\(3A=n.\left(n+1\right).\left(n+2\right)\)
\(A=\dfrac{n.\left(n+1\right).\left(n+2\right)}{3}\)
c)
\(B=1.2.3+2.3.4+...+\left(n-1\right).n.\left(n+1\right)\)
\(4B=1.2.3.4+2.3.4.4+3.4.5.4+...+\left(n-1\right).n.\left(n+2\right).4\)
\(4B=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+...+\left(n-1\right).n.\left(n+1\right).\left[\left(n+2\right)-\left(n-2\right)\right]\)\(4B=1.2.3.4+\left(2.3.4.5-1.2.3.4\right)+\left(3.4.5.6-2.3.4.5\right)+...+\left[\left(n-1\right).n.\left(n+1\right).\left(n+2\right)-\left(n-1\right).n.\left(n+1\right).\left(n-2\right)\right]\)\(4B=\left(n-1\right).n.\left(n+1\right).\left(n+2\right)\\ B=\dfrac{\left(n-1\right).n.\left(n+1\right).\left(n+2\right)}{4}\)
1 tính nhanh
A=1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6
B= (100-1)x(100-2)x(100-3)x...x(100-n) Với n là số tự nhiên và tích có đúng 100 thừa số.
3 tính thuận tiện
a) 135x789789-788x135135
b) (28x9696-96x2828) : (1x2x3x4x....x2016)
c) 1+2-3-4+5+6-7-8+...+2009+2010
4 tìm x
a) (x+32)-17) x2=42
b) 125+ (145-x)=175
1 tính nhanh
A=1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6
B= (100-1)x(100-2)x(100-3)x...x(100-n) Với n là số tự nhiên và tích có đúng 100 thừa số.
3 tính thuận tiện
a) 135x789789-788x135135
b) (28x9696-96x2828) : (1x2x3x4x....x2016)
c) 1+2-3-4+5+6-7-8+...+2009+2010
4 tìm x
a) (x+32)-17) x2=42
b) 125+ (145-x)=175
1.
a.
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}=1-\frac{1}{6}=\frac{5}{6}\)
b.
Tích có 100 thừa số
=> n = 100
\(\left(100-1\right)\times\left(100-2\right)\times\left(100-3\right)\times...\times\left(100-99\right)\times\left(100-100\right)\)
\(=\left(100-1\right)\times\left(100-2\right)\times\left(100-3\right)\times...\times\left(100-99\right)\times0\)
\(=0\)
2.
a.
\(135\times789789-789\times135135=1001\times\left(135\times789-789\times135\right)=1001\times0=0\)
b.
\(\left(28\times9696-96\times2828\right)\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=\left[101\times\left(28\times96-96\times28\right)\right]\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=\left(101\times0\right)\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=0\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=0\)
3.
a.
\(\left[\left(x+32\right)-17\right]\times2=42\)
\(\left(x+32\right)-17=\frac{42}{2}\)
\(\left(x+32\right)-17=21\)
\(x+32=21+17\)
\(x+32=38\)
\(x=38-32\)
\(x=6\)
b.
\(125+\left(145-x\right)=175\)
\(145-x=175-125\)
\(145-x=50\)
\(x=145-50\)
\(x=95\)
A=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6
A=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6
A=1-1/6
A=5/6
Vậy: A=5/6
B=(100-1).(100-2).(100-3). ... .(100-n)
B=99.98.97. ... .0
B=0
Vậy B=0
Chắc Vậy
BÀi 1 tính
a, 1+ 2+3 + ... + n
b , 1x2 + 2x3 + 3x4 + ... + 99 x 100
a)
Số số hạng của dãy trên là;
(n - 1) : 1 + 1 = n(số hạng)
Tổng dãy trên là:
(n + 1) x n : 2 = ? (tùy giá trị n)
b) Đặt A = 1x2 + 2x3 + 3x4 + ... + 99 x 100
3A= 3 x ( 1x2 + 2x3 + 3x4 + ... + 99 x 100)
3A = 1 x 2 x (3 - 0) + 2 x 3 x(4-1) + .....+99.100.(101 - 98)
3A = 1 x 2 x 3 - 1 x 2 x 3 + 2 x 3 x 4 - 2 x 3 x 4 + .......+ 99.100.101
3A = 99.100.101
A = \(\frac{\text{99.100.101}}{3}=333300\)
a, 1 + 2 + 3 + ... + n
= ( 1 + n) × n : 2
b, 1×2 + 2×3 + 3×4 + ... + 99×100
= 1/3 × ( 1×2×3 + 2×3×3 + 3×4×3 + ... + 99×100×3)
= 1/3 × [ 1×2×(3-0) + 2×3×(4-1) + 3×4×(5-2) + ... + 99×100×(101-98) ]
= 1/3 × ( 1×2×3 - 0×1×2 + 2×3×4 - 1×2×3 + 3×4×5 - 2×3×4 + ... + 99×100×101 - 98×99×100 )
= 1/3 × [ ( 1×2×3 + 2×3×4 + 3×4×5 + ... + 99×100×101) - ( 0×1×2 + 1×2×3 + 2×3×4 + ... + 98×99×100) ]
= 1/3 × ( 99×100×101 - 0×1×2)
= 1/3 × ( 99×100×101 - 0)
= 1/3 × 99×100×101
= 333 300