3A=1/3^2-1/3^3+...-1/3^2017

3A+A=1-1/3+...-1/3^2015+1/3-1/3^2+...-1/3^2016

4A=1-1/3^2016

4A=3^2016-1/3^2016

A=3^2016-1/4.3^2016

A = 1.2+2.3+...+2016.2017

3A=1.2.3 + 2.3.(4-1) + .. + 2016.2017.(2018-2015)

3A = 1.2.3 + 2.3.4 - 1.2.3 + ... + 2016.2017.2018 - 2015.2016.2017

3A = 2016.2017.2018

A = 2016.2017.2018 : 3 

A = 2735245632

3A=1*2*3+2*3*(4-1)+.........+2016*2017.(2018-2015)

3A=1.2.3-1.2.3+2.3.4-2.3.4+.........+2016.2017.3

3A=2016.2017.2018

KẾT QUẢ TỰ TÍNH

\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{2015.2016}\)

\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{2015}-\frac{1}{2016}\)

\(S=1-\frac{1}{2016}=\frac{2015}{2016}\)

\(S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-........+\frac{1}{2015}-\frac{1}{2016}\)

\(S=\frac{1}{1}-\left(-\frac{1}{2}+\frac{1}{2}\right)+\left(-\frac{1}{3}+\frac{1}{3}\right)+......+\left(-\frac{1}{2015}+\frac{1}{2015}\right)-\frac{1}{2016}\)

\(S=\frac{1}{1}-\frac{1}{2016}=\frac{2015}{2016}\)

2017/2016

S = 1/1x2 + 1/2x3 + 1/3x4 + ... + 1/2014x2015 + 1/2015x2016

S = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... +  1/2014 - 1/2015 + 1/2015 - 1/2016

S = 1 - 1/2016

S = 2015

\(S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-......+\frac{1}{2015}-\frac{1}{2016}\)

\(S=\frac{1}{1}-\frac{1}{2016}=\frac{2015}{2016}\)

S= 1-2 + 3-4 + 5-6+... ..+2015-2016(có 2016 số)

=(1-2) + (3-4) + (5-6) +...+(2015-2016) (có 2016:2=1008 nhóm có 2 số)

=-1      +(-1)   +(-1)    +...+(-1)( có 1008 số(-1))

=-1.1008

=-1008

vậy S=-1008

A = 3¹+3²+3³+3⁴+...+3²⁰¹⁵+3²⁰¹⁶

S=-1008 mình chắc chắn luôn!

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