5x5+1x2+956+546x56=
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Tính
A=1x2x3+2x3x3+3x4x3+4x5x3+....+98x99x3
B=1x2+2x3+3x4+4x5+...+98x99
C=1x1+2x2+3x3+4x4+5x5+...+98x98
A=1.2.3+2.3(4-1)+3.4(5-2)+4.5(6-3)+....+98.99(100-97) "." la dau nhan
A=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
A=1.2.3+98.99.100
A= 970206
Ta có : B = 1.2 + 2.3 + 3.4 + ..... + 98.99
=> 3B = 0.1.2 + 1.2.3 - 1.2.3 + ...... + 98.99.100
=> 3B = 98.99.100
=> B = \(\frac{98.99.100}{3}\) = 323400
A=1x2+2x3+3x4+...+49x50
3A= 3(1.2+2.3+3.4+...+49.50)
3A= 1.2.3+2.3.3+3.4.3+...+49.50.3
3A= 1.2.(3-0)+2.3(4-1)+3.4(5-2)+...+49.50.(51-48)
3A= 0.1.2-1.2.3+1.2.3-2.3.4+2.3.4-3.4.5+...+48.49.50-49.50.51
3A= 49.50.51
A= 49.50.51/3=41650
B=1x3+3x5+5x7+...+99x101
B=1/1.3 +1/3.5 +...+1/99.101
2B=2/1.3 + 2/3.5 +...+2/99.101
2B=1-1/3+1/3-1/5+...+1/99-1/101
2B=1-1/101
2B=100/101
B=100/101:2=100/202
S = 1 x 2 + 2 x 3 + ...... + 99 x 100
3S = 1 x 2 x 3 + 2 x 3 x (4 - 1) + .... + 99 x 100 x (101 - 98)
3S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ..... + 99 x 100 x 101 - 98 x 99 x 100
3S = 99 x 100 x 101 = 999900
S = 999900 : 3 = 333300
Câu 2 bạn ghi rõ đề hơn đi rồi tớ làm cho
1.
\(A=\frac{1.2}{2.2}.\frac{2.3}{3.3}.\frac{3.4}{4.4}......\frac{2012.2013}{2013.2013}\)
\(A=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.........\frac{2012}{2013}\)
\(A=\frac{1.2.3.4.....2012}{2.3.4.5......2013}\)
\(A=\frac{1}{2013}\)
\(B=\frac{2012.2013-2012.2012}{2012.2011+2012.2}\)
\(B=\frac{2012\left(2013-2012\right)}{2012\left(2011+2\right)}\)
\(B=\frac{2013-2012}{2011+2}\)
\(B=\frac{1}{2013}\)
\(Vì:\frac{ 1}{2013}=\frac{1}{2013}\)
\(\Rightarrow\frac{1.2}{2.2}.\frac{2.3}{3.3}.\frac{3.4}{4.4}......\frac{2012.2013}{2013.2013}=\frac{2012.2013-2012.2012}{2012.2011+2012.2}\)
\(Hay: A=B\)
\(A=\frac{1\times2}{2\times2}\times\frac{2\times3}{3\times3}\times\frac{3\times4}{4\times4}\times\frac{4\times5}{5\times5}\times...\times\frac{2012\times2013}{2013\times2013}\)
\(\Rightarrow A=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times...\times\frac{2012}{2013}\)
\(\Rightarrow A=\frac{1\times2\times3\times4\times...\times2012}{2\times3\times4\times5\times...\times2013}\)
\(\Rightarrow A=\frac{1}{2013}\)
\(B=\frac{2012\times2013-2012\times2012}{2012\times2011+2012\times2}\)
\(\Rightarrow B=\frac{2012\times\left(2013-2012\right)}{2012\times\left(2011+2\right)}\)
\(\Rightarrow B=\frac{2012\times1}{2012\times2013}\)
\(\Rightarrow B=\frac{1}{2013}\)
a)(y+2):5-5x5=378
(y+2):5-25=378
(y+2):5=378+25
(y+2):5=403
(y+2)=403x5
y+2=2015
y=2015-2
y=2013
(y+2):5-5.5=378
(y+2):5-25=378
(y+20)=378+25
(y+2)=403
(y+2)=403.5
y+2=2015
y=2015-2
y=2013
=31559
31559