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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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5B = 1/11 - 1/16 + 1/16 - 1/21 + 1/21 - 1/26 +.........+ 1/56 - 1/61 +1/61 - 1/66
5B = 1/11 - 1/66
5B = 5/66
B = 1/66
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A = 1 × 6 + 6 × 9 + 11 × 16 + 16 × 19 + 21 × 26
= 6 + 54 + 176 + 304 + 546
= 1086
Vậy chữ số tận cùng của A là 6
A=(...6)+(...4)+(.....6)+(....4)+(....6)
A=(....6)
vậy chữ số tận cùng của A bằng 6
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\(\left(\frac{2010:x-6}{2011}+\frac{3}{4}\right)x\frac{11}{3}=1\)
\(\frac{2010:x-6}{2011}+\frac{3}{4}=\frac{3}{11}\)
\(\frac{2010:x-6}{2011}=-\frac{21}{44}\)
\(\Rightarrow44\left(2010:x-6\right)=\left(-21\right).2011\)
\(\Rightarrow88440:x-264=-42231\)
\(\Rightarrow88440:x=-41967\)
\(\Rightarrow x=\frac{88440}{-41967}\approx2,108\)
\(\left(\frac{2010x-6}{2011}+\frac{3}{4}\right)\times\frac{11}{13}=1\)
\(\frac{2010x-6}{2011}+\frac{3}{4}=\frac{11}{13}\)
\(\frac{2010x-6}{2011}=\frac{11}{13}-\frac{3}{4}\)
\(\frac{2010x-6}{2011}=\frac{5}{52}\)
\(\left(2010x-6\right)\div2011=\frac{5}{52}\)
\(2010x-6=\frac{5}{52}\times2011\)
\(2010x-6=\frac{10055}{52}\)
\(2010x=\frac{10055}{52}+6\)
\(2010x=\frac{10367}{52}\)
\(x=\frac{10367}{52}:2010\)
\(x=\frac{10367}{104520}\)
\(C=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{2011.2016}\)
\(5C=\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+...+\frac{5}{2011.2016}\)
\(5C=1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{2011}-\frac{1}{2016}\)
\(5C=1-\frac{1}{2016}\)
\(5C=\frac{2015}{2016}\)
\(C=\frac{2015}{2016}:5\)
\(C=\frac{403}{2016}\)
Đặt A = \(\frac{1}{1\times6}+\frac{1}{6\times11}+\frac{1}{11\times16}+...+\frac{1}{2011\times2016}\)
\(A\times5=\frac{5}{1\times6}+\frac{5}{6\times11}+\frac{5}{11\times16}+...+\frac{5}{2011\times2016}\)
\(A\times5=\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{2011}-\frac{1}{2016}\)
\(A\times5=\frac{1}{1}-\frac{1}{2016}\)
\(A=\frac{2015}{2016}\times\frac{1}{5}\)
\(A=\frac{2015}{10080}=\frac{403}{2016}\)