Tính (1.2+2.3+3.4+...2012.2013)-(2^2+3^2+...+2013^2)
Những câu hỏi liên quan
(1.2+2.3+3.4+.....+2012.2013)-(22+32+42+......+20132)
Tính nhanh
(1.2+2.3+3.4+.....+2012.2013)-(22+32+42+......+20132)
= 1.2 + 2.3 + 3.4 +...+ 2012.2013 - 22 -32 - 42 -....-20132
=1.2 + 2.3 + 3.4 + ...+2012.2013 - 2.2 -3.3 - 4.4 -...- 2013.2013
=(1.2 - 2.2) + (2.3 - 3.3) + (3.4 - 4.4) + ...+(2012.2013 - 2013.2013)
=2.(1-2) + 3.(2-3) + 4.(3-4) +...+2013.(2012-2013)
=2.(-1) + 3.(-1) + 4.(-1) + ...+2013.(2012-2013)
= -2 - 3 - 4 -...- 2013
= -(2+3+4+...+2013)
= -[(2013+2).2012:2]
=-2027090
Đúng 0
Bình luận (0)
( 1.2 + 2.3 + 3.4 + ....... + 2012.2013) - ( 22 + 32 + 42 + 52 ........ + 20132 )
(1.2 + 2.3 + 3.4 + ... + 2012.2013) - (22 + 32 + 42 + 52 + ... + 20132)
= [(2 - 1).2 + (3 - 1).3 + (4 - 1).4 + ... + (2013 - 1).2013] - (22 + 32 + 42 + 52 + ... + 20132)
= (22 - 2 + 32 - 3 + 42 - 4 + ... + 20132 - 2013) - (22 + 32 + 42 + 52 + ... + 20132)
= 22 - 2 + 32 - 3 + 42 - 4 + ... + 20132 - 2013 - 22 - 32 - 42 - 52 - ... - 20132
= (22 - 22) + (32 - 32) + (42 - 42) + ... + (20132 - 20132) - (2 + 3 + 4 + ... + 2013)
= 0 - (2 + 3 + 4 + ... + 2013)
= 0 - (1 + 2 + 3 + 4 + ... + 2013) + 1
= 0 - \(\dfrac{2013.\left(2013+1\right)}{2}\) + 1
= 0 - 2027091 + 1
= (-2027091) + 1
= -2027090
Đúng 0
Bình luận (0)
1.Thực hiện phép tính một cách hợp lý:
a,(1.2+2.3+3.4+...+2012.2013)-(\(^{2^2+3^2+4^2+...+2013^2}\))
Tính nhanh:
(1.2+2.3+3.4+....+2012.2013)-(2.2+3.3+4.4+...+2013.2103)
tính tổng M=1.2+2.3+3.4+........+2012.2013
Ta có:
3M=1.2.3+2.3.3+3.4.3+...+2012.2013.3
3M=1.2.3+2.3.(4-1)+3.4.(5-2)+...+2012.2013.(2014-2011)
3M=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+2012.2013.2014-2011.2012.2013
3M=2012.2013.2014
3M=8157014184
M=8157014184:3
M=2719004728
Tín (1.2+2.3+3.4+4.5+.......+2012.2013)-(2.2+3.3+4.4+5.5+.......+2013.2013)
Tính :
a) ( 12 + 22 + 32 +....+ 492 ) - ( 1.2 + 2.3 + 3.4+....+ 49.50 )
b) Tính A - B =... biết A =1.2 + 2.3 + 3.4 + ...+ 98.99 và B = 1^2 + 2^2 + 3^2 +...+98^2?
Xem thêm câu trả lời
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
Đúng 0
Bình luận (0)
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 >:)!!!!!
Đúng 0
Bình luận (0)
Tính tổng :
\(S=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{2012.2013}+\frac{2}{2013.2014}\)
\(\frac{1}{2}S=\frac{1}{2}\left(\frac{2}{2.3}+\frac{2}{3.4}+.....+\frac{2}{2013.2014}\right)\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{2013.2014}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{2013}-\frac{1}{2014}\)
\(=\frac{1}{2}-\frac{1}{2014}=\frac{503}{1007}\)
=> S = 503\(\frac{503}{1007}:\frac{1}{2}=\frac{503}{1007}.2=\frac{1006}{1007}\)
Đúng 0
Bình luận (0)