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A = 1.100 + 2.99 + 3.98 + 98.3 + 99.2 + 100.1
1.100 = 1.100 = 1.100
2.99 = 2.(100 - 1) = 2.100 - 1.2
3.98 = 3.(100 - 2) = 3.100 - 2.3
4.97 = 4.(100 - 3) = 4.100 = 3.4
...............................................................
100.1 = 100.(100 - 99) = 100.100 - 99.100
Cộng vế với vế ta có:
A = 1.100+2.100+...+99.100+100.100 - (1.2 +2.3+ 3.4+...+99.100)
Đặt B = 1.100 + 2.100+...+99.100 + 100.100
C = 1.2 + 2.3 + 3.4 +...+ 99.100
A = B - C
B = 1.100 + 2.100 + ...+ 99.100 + 100.100
B = 100.(1+ 2+ ... + 99+ 100)
B = 100.(100 + 1) x 100 : 2
B = 505000
C = 1.2 + 2.3 + 3.4 +...+ 99.100
3C = 1.2.3 + 2.3.3 +..+99.100.3
1.2.3 = 1.2.3
2.3.3 = 2.3.(4 - 1) = 2.3.4 - 1.2.3
99.100.3 = 99.100.(101 - 98)=99.100.101-98.99.100
Cộng vế với vế ta có:
3C = 99.100.101
C = 99.100.101 : 3
C = 333300
A = B - C
A = 505000 - 333300
A = 171700
Câu b:
A = 9+99+ 999+...+9999...99(1000 chữ số 9)
9 = - 1 + 10
99 = - 1 + 100
999 = - 1 + 1000
...............................
999...999 = -1 + 1000...00(1000 chữ số 0)
Cộng vế với vế ta có:
B = - 1 x 1000 + 11111...10(1000 chữ số 1)
B = 111....110110 (999 chữ số 1)
Câu 2:
A = 1.3 + 3.5 + 5.7 + ...+ 97.99 + 99.100
A = (1.3 + 3.5 + 5.7 + ...+ 97.99) + 99.100
Đặt B = 1.3 + 3.5 + 5.7 + ...+ 97.99
6B = B = 1.3 + 3.5 + 5.7 + ...+ 97.99
6B = 1.3.6 + 3.5.6 + ...+ 97.99.6
6B = 1.3.(5+1) . 3.5.(7-1) + ..+97.99.(101-95)
6B = 1.3.5 + 1.3.1 +3.5.7- 1.3.5 +...+97.99.101-95.99.97
6B = 1.3.1 + 97.99.101
6B = 3 + 969903
6B = 969906
B = 969906 : 6
B = 161651
A = 161651 + 99.100
A = 161651 + 9900
A = 171551
Câu 3:
A = A = 2.4 + 4.6 + 6.8 +...+ 98.100 + 100.102
6A = 2.4.6 + 4.6.6 +..+98.100.6 + 100.102.6
6A = 2.4.6 + 4.6.(8-2) +...+100.102.(104 - 98)
6A = 2.4.6 + 4.6.8 - 2.4.6 + ...+ 100.102.104 - 98.100.102
6A = 100.102.104
A = 100.102.104 : 6
A = 10200.104 : 6
A = 1060800 : 6
A = 176800
b) B = 22 + 42 + 62 + ... + 982
\(\frac{1}{4}B=1^2+2^2+3^2+...+49^2\)
\(\frac{1}{4}B=1+2\left(1+1\right)+3\left(2+1\right)+...+49\left(48+1\right)\)
\(\frac{1}{4}B=1+2+1.2+2.3+3+...+48.49+49\)
\(\frac{1}{4}B=\left(1+2+3+...+49\right)+\left(1.2+2.3+...+48.49\right)\)
đặt A = 1.2 + 2.3 +...+ 48.49 ta có:
A = 1.2 + 2.3 +...+ 48.49
3A = 1.2.3 + 2.3.( 4 - 1) + ... + 48.49.( 50 - 47 )
3A = 1.2.3 + 2.3.4 - 1.2.3 +...+ 48.49.50 - 47.48.49
3A = 48.49.50
A = \(\frac{48.49.50}{3}=39200\)
thay A = 39200 vào \(\frac{1}{4}B\) ta có:
\(\frac{1}{4}B=\left(1+2+3+...+49\right)+39200\)
\(\frac{1}{4}B=1225+39200\)
\(\frac{1}{4}B=40425\)
B = 40425.4
B = 161700
vậy B = 161700
3A=1.2.3+2.3.4+3.4.3+.......+99.100.3
3A=1.2.(3-0) + 2.3 (4-1) + 3.4 . (5-2)+.......+ 99.100(101-98)
3A=(1.2.3+2.3.4+3.4.5+......+98.99.100)-(0.1.2+1.2.3+.....+98.99.100)
3A=99.100.101-0
3A=999900
A=999900:3
A=333300
1.Tính
A= (1-1/22).(1-1/32)...(1-1/1002)
B= -1/1.2-1/2.3-1/3.4-...-1/100.101
C= 1.2+2.3+3.4+...+100.101
Lời giải :
Đặt S=1.2+2.3+3.4+4.5+…+99.100+100.101
3S=1.2.3+2.3.3+3.4.3+4.5.3+…+99.100.3+100.101.3
=1.2(3−0)+2.3(4−1)+3.4(5−2)+4.5(6−3)+…+99.100(101−98)+100.101(102−99)
=0.1.2-1.2.3+1.2.3-2.3.4+...+99.100.101-100.101.102
=100.101.102
S=100.101.34=343400
1.Tính
a) Ta có:
A=(1-1/22).(1-1/32)...(1-1/1002)
=>A=3/22.8/32.....9999/1002
=>A=(1.3/2.2).(2.4/3.3).....(99.101/100.100)
=>A=(1.2.3.....99/2.3.4.....100).(3.4.5.....101/2.3.4.....100)
=>A=1/100.101/2
=>A=101/200
b) Ta có:
B=-1/1.2-1/2.3-1/3.4-...-1/100.101
=>B=-(1/1.2+1/2.3+1/3.4+...+1/100.101)
=>B=-(1-1/2+1/2-1/3+1/3-1/4+...+1/100-1/101)
=>B=-(1-1/101)
=>B=-100/101
c) Ta có:
C=1.2+2.3+3.4+...+100.101
=>3C=1.2.3+2.3.3+3.4.3+...+100.101.3
=>3C=1.2.3+2.3.(4-1)+3.4.(5-2)+...+100.101.(102-99)
=>3C=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-3.4.5+...+100.101.102
=>3C=100.101.102
=>3C=1030200
=>C=343400
Chúc bạn hok tốt nhé >:)!!!!!