\(...A=\left(-\dfrac{1}{2}\right).\left(-\dfrac{2}{3}\right).\left(-\dfrac{3}{4}\right)....\left(-\dfrac{1998}{1999}\right).\)

Số dấu trừ là : \(\left(1998-1\right):1+1=1998\) là số chẵn

\(\Rightarrow A=\dfrac{1.2.3...1998}{2.3.4...1999}\)

\(\Rightarrow A=\dfrac{1}{1999}\)

gợi ý nè

tính hết mấy cái hiệu trong ngoặc rồi nhân lại

vì kết thúc ở số 1999

nên sẽ có 1999 dấu -

nên kq là âm

nhân ra rồi triệt tiêu đi

\(A=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+.....+\frac{1}{2018}\left(1+2+3+...+2018\right)\)

\(=1+\frac{1}{2}\cdot\frac{2.\left(2+1\right)}{2}+\frac{1}{3}\cdot\frac{3.\left(3+1\right)}{2}+...+\frac{1}{2018}\cdot\frac{2018\left(2018+1\right)}{2}\)

\(=1+\frac{3}{2}+\frac{4}{2}+....+\frac{2019}{2}\)

\(=\frac{2+3+4+...+2019}{2}\)

\(=\frac{\frac{2019\left(2019+1\right)}{2}-1}{2}=1019594.5\)

\(\Leftrightarrow\left(\frac{1}{2}\right)^{x+1}=\frac{-3}{8}+\frac{1}{2}\)(tự quy đồng)

\(\Leftrightarrow\left(\frac{1}{2}\right)^{x+1}=\frac{1}{8}\)

\(\Leftrightarrow\left(\frac{1}{2}\right)^{x+1}=\left(\frac{1}{2}\right)^3\)
\(\Leftrightarrow x+1=3\)

\(\Leftrightarrow x=3-1\)

\(\Leftrightarrow x=2\)

ta có ( 1/2 )^{x + 1} = 1/2 suy ra x +1 = 1 Nên x = 0

2016/1+....+1/2016=(1+2015/2)+(1+2014/3)+.....+(1+1/2016)

=2017/2+2017/3+......+2017/2017

=2017.(1/2+1/3+....+1/2017)

=> 

1/2+1/3+1/4+...+1/2017

                                                                  =1

2016/1+2015/2+2014/3+......+1/2016

làm gif có a/b mà tính

a)\({-1\over 2}x^2×y^2 - x^2×y^2 +{2\over 3} x^2×y^2 \)

=\(({ -1\over 2}-1+{ 2\over 3})x^2×y^2\)

=\({-5 \over 6}x^2×y^2\)

b)\({1 \over 2}a^3×b^2 +{4 \over 3}3ab^2 × {1 \over 2}a^2\)

=\({1 \over 2}a^3×b^2 +({4 \over 3}× {1 \over 2})3b^2 (a×a^2) \)

=\({1 \over 2}a^3×b^2 +{2 \over 3}3a^3b^2\)

=\(({1 \over 2} +{2 \over 3}3)a^3b^2\)

=\({5 \over 2}a^3b^2\)

c)

a) 3/13 - 3/2 + 10/13

= (3/13 + 10/13) - 3/2

= 1 - 3/2

= -1/2

b) 4/7 - (-2/7) - 7/3

= 4/7 + 2/7 - 7/3

= 6/7 - 7/3

= -31/21

c) 2/3 - (-1/6) + 5/4

= 2/3 + 1/6 + 5/4

= 8/12 + 2/12 + 15/12

= 25/12

a, 3/13 - 3/2 + 10/13

= 3/13 + 10/13

= 1 - 3/2 = -1/2

b,4/7 - (-2/7) - 7/3

= 4/7 + 2/7 - 7/3

= 6/7 - 7/3

= 18/21 - 14/21

= 4/21

c, 2/3 - -1/6 +5/4 

= 2/3 + 1/16 +5/4

= 128/192 + 12/192 + 240/192

= 380/192

= 95/4 

không hiểu chỗ nào hỏi tui