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\(C=1.2+2.3+3.4+...+x.\left(x-1\right)\)
\(\Rightarrow3C=1.2.3+2.3.3+3.4.3+...+x.\left(x-1\right).3\)
\(\Rightarrow3C=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+x.\left(x-1\right).\left[\left(x+1\right)-\left(x-2\right)\right]\)
\(\Rightarrow3C=\left(1.2.3-0.12\right)+\left(2.3.4-1.2.3\right)+\left(3.4.5-2.3.4\right)+...+\left[x.\left(x-1\right)\left(x+1\right)-x.\left(x-1\right)\left(x-2\right)\right]\)
\(\Rightarrow3C=-0.1.2+x.\left(x-1\right)\left(x+1\right)\)
\(\Rightarrow3C=x.\left(x-1\right)\left(x+1\right)\)
\(\Rightarrow C=\dfrac{x.\left(x-1\right)\left(x+1\right)}{3}\)
3C=1x2x3+2x3x3+3x4x3+...+Xx(X+1)=
=1x2x3+2x3x(4-1)+3x4x(5-2)+...+Xx(X+1)[(X+2)-(X-1)]=
=1x2x3-1x2x3+2x3x4-2x3x4+3x4x5-...-(X-1)xXx(X+1)+Xx(X+1)x(X+2)=
=Xx(X+1)(X+2)
gọi biểu thức trên là A, ta có :
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
**** nha ^^
Gọi biểu thức trên là A, ta có :
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
P=1x2+2x3+3x4+...+2017x2018
3P = 1x2x3 + 2x3x3 + 3x4x3 + ... + 2017x2018x3
3P = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + ... +2017x2018x(2019-2016)
3P = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + ... + 2017x2018x2019 - 2016x2017x2018
3P = 2017x2018x2019
P = 2017x2018x2019 : 3
P = 2739315938
P = 1x2+2x3+3x4+...+2017x2018
3xP = 1x2x3+2x3x3+3x4x3+...+2017x2018x3
3xP = 1x2x3+2x3x(4-1)+3x4x(5-2)+...+2017x2018x(2019-2016)
3xP = 1x2x3+2x3x4-2x3x1+3x4x5-3x4x2+...+2017x2018x2019-2017x2018x2016
3xP = 2017x2018x2019
3xP = 8217947814
P = 8217947814 : 3
P = 2739315938
1.2+2.3+3.4+4.5+............+99.100
=2+6+12+20+.............+9900
dãy số trên có số các số hạng là:
mìk chỉ làm đc đến đây thôi
A = 1 x 2 + 2 x 3 + 3 x 4 + . . . + 99 x 100
3A = 1 x 2 x 3 + 2 x 3 x ( 4 - 1 ) + 3 x 4 x ( 5 - 2 ) + . . . + 99 x 100 x ( 101 - 98 )
3A = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3 x 4 + . . . + 99 x 100 x 101 - 98 x 99 x 100
3A = 99 x 100 x 101
A = 99 x 100 x 101 : 3
A = 33 x 100 x 101
A = 333300
a) 1/1x5 + ... + 1/21x25
= 4 x (1-1/5 + 1/5 - 1/9 + ... + 1/21 - 1/25)
= 1/4 x (1 - 1/25)
= 1/4 x 24/25
= 6/25
M=1.2+2.3+3.4+...+19.20
3.M=1.2.3+2.3.3+3.4.3+...+19.20.3
3.M=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+19.20.(21-18)
3.M=(1.2.3-0.1.2)+(2.3.4-1.2.3)+(3.4.5-2.3.4)+...+(19.20.21-18.19.20)
Những cái bị gạch là giản ước.
3.M=19.20.21-0.1.2
3.M=7980-0
3.M=7980
M=7980:3
M=2660
Vậy M=2660
Dấu . là dấu nhân
\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2017}-\frac{1}{2018}\)
\(S=1-\frac{1}{2018}\)
\(S=\frac{2018}{2018}-\frac{1}{2018}\)
\(S=\frac{2017}{2018}\)
\(S=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{2017.2018}.\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{2017}+\frac{1}{2017}-\frac{1}{2018}\)
\(=1-\frac{1}{2018}=\frac{2017}{2018}\)
sai một chỗ
\(A=1.2+2.3+3.4+...+18.19\)
\(\Leftrightarrow3A=1.2.3+2.3.3+3.4.3+...+18.19.3\)
\(\Leftrightarrow3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+18.19.\left(20-17\right)\)
\(\Leftrightarrow3A=1.2.3+2.3.4-1.2.3+...+18.19.20-17.18.19\)
\(\Leftrightarrow3A=18.19.20\)
\(\Leftrightarrow A=6.19.20\)
1.2 + 2.3 + 3.4 +…+ 99.100
= 1+ (1.2 + 2) + (2.3 + 3) + (3.4 + 4) +…+ (99.100 + 100) – (1 + 2 + 3 + 4 +…+ 100)
= 12 + 22 + 32 + 42 +…+ 1002 – (1 + 100).100:2
= 100.(100 + 1).(2.100 + 1):6 – 101.100:2
= 333300
giải từng bước 1 nha cho mk chép