Tính nhanh

2016+84+101+91+99

2016+83x2017+2017x16

2016+84+101+91+99

=(2016+84)+(101+99)+91

=2100+200+91

=2391

2016+83x2017+2017x16

=2017-1+83x2017+2017x16

=2017x(1+83+16)-1

=2017x100-1

=201701

2016+84+101+91+99

=(2016+84)+(101+99)+91

=2100+200+91

=2391

2016+83x2017+2017x16

=2017-1+83x2017+2017x16

=2017x(1+83+16)-1

=2017x100-1

=201701

2016 + 84 + 101 + 91 + 99

= ( 2016 + 84 ) + ( 101 + 99 ) + 91

= 2100 + 200 + 91

= 2300 + 91

= 2391

2016 + 83 x 2017 + 2017 x 16

= 2017 x ( 83 + 16 ) + 2016

= 2017 x 99 + 2016

= 199683 + 2016

= 201699

k mk nha

a, = 2017/2016.(1+1/2015) = 2017/2016.2016/2015 = 2017/2015

b, = -9/101-9/102-9/101+9/102 = -18/101

k mk nha

\(2^{2016}+4^{2016}+6^{2016}+...+20^{2016}=2^{2016}\left(1+2^{2016}+3^{2016}+...+10^{2016}\right)\)

Do đó:

\(A=\frac{1^{2016}+2^{2016}+3^{2016}+...+10^{2016}}{2^{2016}+4^{2016}+6^{2016}+...+20^{2016}}=\frac{1}{2^{2016}}\)

a, \(=2017\left(\frac{1}{2016}+\frac{1}{2015.2016}\right)\)

\(=2017\left(\frac{2015+1}{2016}\right)\)

=2017.1=2017

b, = -9/101-9/102-9/101+9/102

=-18/101

2016-101=1915

kq do

Số số hạng dãy số trên là :
( 2016 - 101 ) : 1 + 1 = 1916

 Đáp số : 1916

Công thức : ( Số cuối - số đầu ) : KC + 1

Nhớ k mk

\(P=\frac{3^{2016}-6^{2016}+9^{2016}-12^{2016}+15^{2016}-18^{2016}}{-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}}\)

\(=\frac{\left(1.3\right)^{2016}-\left(2.3\right)^{2016}+\left(3.3\right)^{2016}-\left(4.3\right)^{2016}+\left(5.3\right)^{2016}-\left(6.3\right)^{2016}}{-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}}\)

\(=\frac{1^{2016}.3^{2016}-2^{2016}.3^{2016}+3^{2016}.3^{2016}-4^{2016}.3^{2016}+5^{2016}.3^{2016}-6^{2016}.3^{2016}}{-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}}\)

\(=\frac{-3^{2016}\left(-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}\right)}{-1^{2016}+2^{2016}-3^{2016}+4^{2016}-5^{2016}+6^{2016}}\)

\(=-3^{2016}\)

Bằng \(-\frac{2}{11}\)