c: C=1*2+2*3+3*4+...+58*59+59*60

=>3*C=1*2*3+2*3*(4-1)+3*4*(5-2)+...+58*59(60-57)+59*60(61-58)

=>3*C=1*2*3+2*3*4-1*2*3+...+58*59*60-58*59*57+59*60*61-58*59*60

=>3*C=59*60*61

=>C=59*20*61=71980

Xét: 3/(1.2)=(1+2)/(1.2)=1/2+1

5/(2.3)=(2+3)/(2.3)=1/3+/1/2

7/(3.4)=(3+4)/(3.4)=1/4+1/3

...

2021/(1010.1011)=(1010+1011)/(1010.1011)=1/1010+1/1011

Do đó: Q=1+1/2-1/2-1/3+1/3+1/4-...-1/1010-1/1011

=1-1/1011

=1010/1011

sai thì sorry nha, nhưng cách làm là đúng rồi

Lê Gia Long e lớp 4 thì ko đc lm!

\(Q=\frac{3}{1\cdot2}-\frac{5}{2\cdot3}+\frac{7}{3\cdot4}...-\frac{2021}{1010\cdot1011}\)

\(=\left(\frac{1}{1}+\frac{1}{2}\right)-\left(\frac{1}{2}+\frac{1}{3}\right)+\left(\frac{1}{3}+\frac{1}{4}\right)...-\left(\frac{1}{1010}-\frac{1}{1011}\right)\)

\(=1-\frac{1}{1011}\)

\(=\frac{1010}{1011}\)

Đặt A = 1.2 + 2.3 + 3.4 + ...... + 99.100

 3A=1.2.3 - 1.2.3 + 2.3.4 - 2.3.4  + .....+99.100.101

3A=99.100.101

A=99.100.101/3=333300

Đặt A = 1.2 + 2.3 + 3.4 + ...... + 99.100

 3A=1.2.3 - 1.2.3 + 2.3.4 - 2.3.4  + .....+99.100.101

3A=99.100.101

A=99.100.101/3=333300

Đặt \(A=7^5+7^6+...+7^{100}\)

\(7A=7^6+7^7+...+7^{101}\\7A-A=(7^6+7^7+...+7^{101})-(7^5+7^6+...+7^{100})\\6A=7^{101}-7^5\\\Rightarrow A=\dfrac{7^{101}-7^5}{6}\)

A=67101−75​
 

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1a) x - 1/3 = 13/6

          x  = 13/6 + 1/3

          x  = 5/2

b) -7/5 - x = 13/7 : 13/7

    -7/5 - x = 1

             x = -7/5 - 1

             x = -12/5

2) A = 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/2015.2016

A = 1 -1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2015 - 1/2016

A = 1 - 1/2016

A = 1 - 1/2016

A = 2015/2016

bạn hãy hãy cộng theo cặp cho dễ nhé,có 50 cặp như thế do đó là 101*50=5050

101 ở đâu vậy bn