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\(a,A=1\cdot2+2\cdot3+...+98\cdot99\\ 3A=1\cdot2\cdot3+2\cdot3\cdot3+3\cdot4\cdot3+...+98\cdot99\cdot3\\ 3A=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+3\cdot4\left(5-2\right)+...+98\cdot99\left(100-97\right)\\ 3A=1\cdot2\cdot3-1\cdot2\cdot3+2\cdot3\cdot4-2\cdot3\cdot4+3\cdot4\cdot5-...-97\cdot98\cdot99+98\cdot99\cdot100\\ 3A=98\cdot99\cdot100=970200\\ A=323400\)
\(b,B=1^2+2^2+3^3+...+98^2\\ B=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+98\left(99-1\right)\\ B=\left(1\cdot2+2\cdot3+3\cdot4+...+98\cdot99\right)-\left(1+2+...+98\right)\\ B=323400-\left[\left(98+1\right)\left(98-1+1\right):2\right]\\ B=323400-4851=318549\\ c,C=1\cdot99+2\left(99-1\right)+3\left(99-2\right)+...+98\left(99-97\right)+99\left(99-98\right)\\ C=1\cdot99+2\cdot99-1\cdot2+3\cdot99-2\cdot3+...+98\cdot99-97\cdot98+99\cdot99-98\cdot99\\ C=99\left(1+2+...+99\right)-\left(1\cdot2+2\cdot3+...+98\cdot99\right)\\ C=99\left[\left(99+1\right)\left(99-1+1\right):2\right]-323400\\ C=490050-323400=166650\)
https://hoc24.vn/cau-hoi/a-tinh-tong-a1223349899b-su-dung-ket-qua-cau-a-tinh-b122232972982c-su-dung-ket-qua-cau-a-tinh-c1992983979829.2030286199021
:vv hỏi hoài z?
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
a)\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}=\frac{\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(3.2\right)^8.2^2.5}=\frac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+3^8.2^8.2^2.5}=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+3^8.2^{10}.5}\)
\(=\frac{2^{10}.3^8.\left(1-3\right)}{2^{10}.3^8.\left(1+5\right)}=\frac{-2}{6}=\frac{-1}{3}\)
b) đặt A=2100 - 299 + 298 - 297 +...+ 22 - 2
=>2A=2101-2100+299-298+...+23-22
=>2A+A=2101-2100+299-298+...+23-22+2100 - 299 + 298 - 297 +...+ 22 - 2
=>3A=2101-2
=>A=\(\frac{2^{101}-2}{3}\)
\(A=1.2^2+2.3^2+...+98.99^2\)
\(=1.2.\left(3-1\right)+2.3.\left(4-1\right)+...+98.99.\left(100-1\right)\)
\(=1.2.3-1.2+2.3.4-2.3+...+98.99.100-98.99\)
\(=\left(1.2.3+2.3.4+...+98.99.100\right)-\left(1.2+2.3+...+98.99\right)\)
\(=\dfrac{98.99.100.101}{4}+\dfrac{98.99.100}{3}\)
\(=24497550+323400\)
\(=24820950\)
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 >:)!!!!!