A=(0-1-2+3)+(4-5-6+7)+...+((2012-2013-2014+2015)+2016

A=0+0+...+0

A=2016

Vậy A=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!

nhớ k nha

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

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

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

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

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

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

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

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

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

\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2015}}+\frac{1}{2^{2016}}\)

\(2A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.......+\frac{1}{2^{2015}}\)

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

=>\(A=1-\frac{1}{2^{2016}}\)

=>\(A=\frac{2^{2016}-1}{2^{2016}}\)

Ta có : \(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+.....+\frac{1}{2^{2016}}\)

\(\Rightarrow2A=1+\frac{1}{2}+\frac{1}{2^2}+......+\frac{1}{2^{2016}}\)

\(\Rightarrow2A-A=1-\frac{1}{2^{2016}}\)

\(\Rightarrow A=1-\frac{1}{2^{2016}}\)

ta có : 2A = 2 . ( 1 + 1/2^2 + 1/2^3 + ... + 1/2^2016 )

= 1 + 1/2 + 1/2^2 + ... + 1/2^2017

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

=1 - 1/2^2016 = 2^2016 - 1/2^2016

đến đây ko tính được nữa, bạn cứ dữ đáp án này là được!

1/1*2+1/2*3+...+1/2014*2015

=1-1/2+1/2-1/3+..+1/2014-1/2015

=1-1/2015

=2014/2015

kết bạn với mình luôn nhé

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