1/2013 – 1/(2013*2012) – 1/(2012*2011) – 1/(2011*2010) -…. -1/(3*2) – 1/(2*1) 18/08/2021 Bởi Vivian 1/2013 – 1/(2013*2012) – 1/(2012*2011) – 1/(2011*2010) -…. -1/(3*2) – 1/(2*1)
Đáp án:-2012/2013 Giải thích các bước giải: 1/2013*2012-1/2012*2011-1/2011*2010-…-1/3*2-1/2*1=-(1/1*2+1/2*3+…+1/2010*2011+1/2011*2012+1/2012*2013)=-(1-1/2+1/2-1/3+…+1/2010-1/2011+1/2011-1/2012+1/2012-1/2013)=-(1-1/2013)=-2012/2013 Bình luận
Đáp án: \[\frac{{ – 2011}}{{2013}}\] Giải thích các bước giải: Ta có: \[\frac{1}{{n\left( {n + 1} \right)}} = \frac{{\left( {n + 1} \right) – n}}{{n\left( {n + 1} \right)}} = \frac{{n + 1}}{{n\left( {n + 1} \right)}} – \frac{n}{{n\left( {n + 1} \right)}} = \frac{1}{n} – \frac{1}{{n + 1}}\] Áp dụng đẳng thức trên ta có: \[\begin{array}{l}\frac{1}{{2013}} – \frac{1}{{2013.2012}} – \frac{1}{{2012.2011}} – …. – \frac{1}{{3.2}} – \frac{1}{{2.1}}\\ = \frac{1}{{2013}} – \left( {\frac{1}{{2012}} – \frac{1}{{2013}}} \right) – \left( {\frac{1}{{2011}} – \frac{1}{{2012}}} \right) – …. – \left( {\frac{1}{2} – \frac{1}{3}} \right) – \left( {1 – \frac{1}{2}} \right)\\ = \frac{1}{{2013}} – \frac{1}{{2012}} + \frac{1}{{2013}} – \frac{1}{{2011}} + \frac{1}{{2012}} – \frac{1}{{2010}} + \frac{1}{{2011}} – ….. – \frac{1}{2} + \frac{1}{3} – 1 + \frac{1}{2}\\ = \frac{2}{{2013}} – 1 = \frac{{ – 2011}}{{2013}}\end{array}\] Bình luận
Đáp án:-2012/2013
Giải thích các bước giải:
1/2013*2012-1/2012*2011-1/2011*2010-…-1/3*2-1/2*1
=-(1/1*2+1/2*3+…+1/2010*2011+1/2011*2012+1/2012*2013)
=-(1-1/2+1/2-1/3+…+1/2010-1/2011+1/2011-1/2012+1/2012-1/2013)
=-(1-1/2013)
=-2012/2013
Đáp án:
\[\frac{{ – 2011}}{{2013}}\]
Giải thích các bước giải:
Ta có:
\[\frac{1}{{n\left( {n + 1} \right)}} = \frac{{\left( {n + 1} \right) – n}}{{n\left( {n + 1} \right)}} = \frac{{n + 1}}{{n\left( {n + 1} \right)}} – \frac{n}{{n\left( {n + 1} \right)}} = \frac{1}{n} – \frac{1}{{n + 1}}\]
Áp dụng đẳng thức trên ta có:
\[\begin{array}{l}
\frac{1}{{2013}} – \frac{1}{{2013.2012}} – \frac{1}{{2012.2011}} – …. – \frac{1}{{3.2}} – \frac{1}{{2.1}}\\
= \frac{1}{{2013}} – \left( {\frac{1}{{2012}} – \frac{1}{{2013}}} \right) – \left( {\frac{1}{{2011}} – \frac{1}{{2012}}} \right) – …. – \left( {\frac{1}{2} – \frac{1}{3}} \right) – \left( {1 – \frac{1}{2}} \right)\\
= \frac{1}{{2013}} – \frac{1}{{2012}} + \frac{1}{{2013}} – \frac{1}{{2011}} + \frac{1}{{2012}} – \frac{1}{{2010}} + \frac{1}{{2011}} – ….. – \frac{1}{2} + \frac{1}{3} – 1 + \frac{1}{2}\\
= \frac{2}{{2013}} – 1 = \frac{{ – 2011}}{{2013}}
\end{array}\]