Question

A=1.2+2.3+3.4+...............+98.99+99.100

B=1.3+2.4+3.5+...............+99.101

C=1.4+2.5+ 3.6+..............+99.102

D=4+12+24+40+..............+1904+19800

E=1+3+6+10+.................+4851+4950

F=6+16+30+48+..............+19600+19998

G=2+5+9+14+.................+4949+5049

H=1.2.3+2.3.4+...............+98.99.100

I=1²+2²+3²+...................+99²+100²

K=2²+4²+6²+......................+98²+100²

L=1²+3²+5²+.......................+97²+99²

M=1²-2²+3²-4²+....................+99²-100²

N=1.2²+2.3²+3.4²+...............+98.99²

P=1.3+3.5+5.7+................+97.99+99.101

Q=2.4+4.6+6.8+................+98.100+100.102

R=1³+2³+3³+4³+.....................+99³+100³

Answer 1

nhiều quá vậy ?

Answer 2

Gọi A là biểu thức ta có: 
CÂU1 :A = 1.2+2.3+3.4+......+99.100 
          3A = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3 
          3A = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98) 
          3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100 
          3A = 99.100.101 
          A = 99.100.101 : 3 
          A = 33.100.101 
          A = 333 300

Answer 3

cau B

B=1.3+2.4+3.5+......+99.101

B=1.(2+1)+2.(3+1)+3.(4+1)+.......+99.(100+1)

B=1.2+1+2.3+2+3.4+3+.......+99.100+99

B=1.2+2.3+3.4+........+99.100+(1+2+3+....+99)

B=99.100.101+(1+\(\frac{\left(2+99\right).98}{2}\))

B=.......

Answer 4

CÂU3 : C=1(2+2)+2(3+2)+3(4+2)+...+99(100+2)

            C=1.2+1.2+2.3+2.2+...+99.100+99.2

            C=(1.2+2.3+...+99.100)+2(1+2+3+...+99)

            C=333300+9900=343200

CÂU4: A=4+12+24+40+...........+19404+19800 

=2(1.2+2.3+3.4+4.5+...+98.99+99.100) 

Xét tổng: B=1.2+2.3+3.4+4.5+...+98.99+99.100 

=> 3B= 1.2.3 + 2.3.3 + 3.4.3 + 4.5.3 +...+ 98.99.3 + 99.100.3 

= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + 4.5.(6 - 3)+...+ 98.99.(100 - 97) + 99.100.(101 - 98) 

= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6- 3.4.5+...+ 98.99.100-97.98.99+99.100.101-98.99.100 

= 99.100.101 

=999900 => B=333300 

A= 2B = 333300.2 = 666600 

Answer 5

 cau C tuong tu

cau D=4+12+24+40+...+1984

D=2.2+2.2.3+2.3.4+2.4.5+.....+2.31.32

D=2(1.2+2.3+3.4+.....+31.32)

D=2.31.32.33

D=65472

Cau L:\(1^2+2^2+3^2+......+99^2+100^2\)

=\(1.1+2.2+3.3+....+100.100\)

=\(1+\left(1+1\right).2+\left(1+2\right).3+.....+\left(1+99\right).100\)

=\(1+2+1.2+3+2.3+....+100+99.100\)

=\(\left(1.2+2.3+3.4+...+99.100\right)+\left(1+2+3+4+...+100\right)\)

=\(99.100.101\)\(+5050\)

=........

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