Tính GTBT:
A=5^2+10^2+15^2+.....+2015^2
B=1^2-2^2+3^2-4^2+.......+2015^2-2016^2
C=10+10^2+10^3+........+10^17
Những câu hỏi liên quan
Tính nhanh
1) 9 x 10 + 10 x 11 + 11 x 12 + ....+ 2015 x 2016
2) 1 x 2 x 3 + 2 x 3 x 4 + 3 x 4 x 5 + ....+ 2015 x 2016 x 2017
1) 9 x 10 + 10 x 11 + 11 x 12 + ....+ 2015 x 2016
=9x10x11-8x9x10+10x11x12-9x10x11+...+2015x2016x2017-2014x2015x2013
=2015x2016x2017-8x9x10
=8193537360
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Tính nhanh:
a, A = 1 + 2 + 4 + 8 +...+ 1024
b, B = 1 + 5 + 25 + 125 + ... + 15625
c, C = 1 / 1 .2 + 1 / 2 .3 + 1 / 3 .4 + .. + 1 / 2015 .2016
d, D = 10 / 1 . 3 + 10 / 3 . 5 + 10 / 5 . 7 + ... + 10 / 2013 . 2015
a/A=1+2+4+8+...+1024
2A=2+4+8+16+....+2048
2A-A=(2+4+8+16+....+2048)-(1+2+4+8+...+1024)
A=2048-1
A=2047
VẬY A=2047
b/B=1+5+25+125+....+15625
5B=5+25+125+625+....+78125
5B-B=(5+25+125+625+....+78125)-(1+5+25+125+....+15625)
4B=78125-1
4B=78124
B=78124:4
B=19531
VẬY B =19531
C=1/1.2+1/2.3+1/3.4+...+1/2015.2016
C=1-1/2+1/2-1/3+1/3-1/4+...+1/2015-1/2016
=1-1/2016
=2015/2016
VẬY C=2015/2016
D/=10/1.3+10/3.5+10/5.7+....+10/2013.2015
=5(2/1.3+2/3.5+2/5.7+...+2/2013.2015)
=5(1-1/3+1/3-1/5+1/5-1/7+..+1/2013-1/2015)
=5(1-1/2015)
=5.2014/2015
=2014/403
VẬY D=2014/403
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a, A = 1 + 2 + 4 + 8 +...+ 1024
\(A=1+2+2^2+2^3+....+2^{10}\)
\(2A=2+2^2+2^3+....+2^{10}+2^{11}\)
\(A=1+2+2^2+2^3+....+2^{10}\)
\(A=2^{11}-1=2047\)
b, B = 1 + 5 + 25 + 125 + ... + 15625
\(B=1+5+5^2+5^3+....+5^6\)
\(3B=5+5^2+5^3+....+5^6+5^7\)
\(B=1+5+5^2+5^3+....+5^6\)
\(2B=5^7-1\Rightarrow B=\frac{5^7-1}{2}=39062\)
d, D = 10 / 1 . 3 + 10 / 3 . 5 + 10 / 5 . 7 + ... + 10 / 2013 . 2015
\(D=\frac{10}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2013.2015}\right)\)
\(D=\frac{10}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(D=\frac{10}{2}.\left(1-\frac{1}{2015}\right)=5.\frac{2014}{2015}=\frac{2014}{403}\)
Câu c thì tương tự
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a) A = 1 + 2 + 4 + 8 + ... + 1024
=> A = 1 + (2 + 4 + 8 + ... + 1024)
có 512 số hạng
=> A = 1 + [(2 + 1024) . 512 : 2]
=> A = 1 + [1026 . 512 : 2]
=> A = 1 + 262656
=> A = 262657
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tinh: 2915a/(ab+2015a+2015) + b/( bc+2015+b) +c/(ac+c+1)
biết (abc-2015)^10 +(a^2b^2c^2-2015^2)^10=0^1980
So sánh
A=3×10^2014+1/10^2015-2
B=3×10^2015+1/10^2016-2
Tính giá trị biểu thức một cách hợp lí:
a)-18+5.6.(-3)-82-2016-10+2.(-10)^2
b) (a-b)-(a+b)-(b+c)+ 3b+2c với a=-15;b+-205;c=2015
bài 1 tìm x biết
a, (x-1):2017+(x-2):2016=(x-3):2015+(x-4):2014
b, 3/(x+2)(x+5) + 5/(x+5)(x+10) + 7 ( x+10)(x+17) = x/ (x+2)(x+17) ( x khác -2, -5 , -10 , -17)
các bạn giúp mik nhé!
Tính A =(5+10+15+...+2015).(2/5:0,5+2.(-0,4)):(1/5+1/10+1/15+...+1/2015)
A = (5+10+15+....+2015) [ 2/5 : 0,5 + 2(-0,4)] : ( 1/5 + 1/10 + 1/15 +....+1/2015)
A= (5+10+15+....+2015) [ 0,8 + ( - 0,8) ] : ( 1/5 + 1/10 + 1/15 +....+1/2015)
A= (5+10+15+....+2015). 0 :( 1/5 + 1/10 + 1/15 +....+1/2015)
A= 0 :( 1/5 + 1/10 + 1/15 +....+1/2015)
A= 0
Tính:
a) 2^5 x 13^12 x 7^8 : 27 x 13^10 x 7^9
b) 2^n x 11 x 3 : 6^n x 3
c) 5^5 x 7 x 9^5 : 15^10
d) 7 x 8^10 x 27^9 - 8 x 9^13 x 2^27 : 7 x 6^26 x 2^2 - 2^4 x 8^3 x 27^9
e) 2^2^1^2015
f) 2015^0^2015^0^2015
72-8/3 bằng bao nhiêu số tự nhiên
Tính
A=1*2+2*3+3*4+4*5+...+99*100
B=7*8*9+8*9*10+9*10*11+...+2015*2016*2017
C=1+3+3^2+3^3+3^4+3^5+...+3^49+3^50
\(A=\frac{99.100.101}{3}=333300\)
\(B=\frac{2015.2016.2017.2018}{4}-\frac{6.7.8.9}{4}=4133639960604\)
\(C=\frac{3^{51}-1}{3}+1\)
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3A= 1.2.3+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+99.100.(101-98)
3A= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+99.100.101-98.99.100
3a= 99.100.101
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