tinh nhanh
2/1*2+2/2*3+...+2/2016*2017
tinh M=2017+2017/1+2+2017/1+2+3+...+2017/1+2+3+...+2016
Tinh :
B=2017 + 2017/1+2 + 2017/1+2+3 + 2017/1+2+3+4 +....+2017/1+2+3+...+2016
tinh A=1*2+2*3+3*4+4*5+...+2015*2016+2016*2017
Cách giải
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
1^2-2^2+3^2-4^2 ... -2016^2+2017^2 tinh nhanh nha
Đặt A=1^2-2^2+......-2016^2+2017^2
-A=2^2-1^2+........+2016^2-2015^2
ÁP dụng A^2-B^2=(A+B)(A-B)
sau đó bạn sẽ tính được A
a^2+b^2+c^2=a^3+b^3+c^3=1. tinh S=a^2+b^2016+c^2017
A= 1+ 2+ 2^2+ 2^3+ ....+. 2^2016.Biet B=2^2017
Tinh B-A
\(A=1+2+2^2+2^3+...+2^{2016}\)
\(\Rightarrow2A=2+2^2+2^3+2^4+...+2^{2017}\)
\(\Rightarrow2A-A=\left(2+2^2+2^3+2^4+...+2^{2017}\right)-\left(1+2+2^2+2^3+....+2^{2016}\right)\)
\(\Rightarrow A=2^{2017}-1\)
K-2016=1+ (1+2)+(1+2+3)+….+(1+2+3+…+2017)/2017*1+2016*2+2015*3+…+2*2016+1*2017
tìm K
tinh
1+20162+20162/20172
Ta co:20162+1=(2016+1)2_2.2016.1=>1+20162+20162/20172=20172_2.2016+20162/20172=(2017-2016/2017)2
thuc hien phep tinh
m=1+(-2)+3+(-4)+...+(-2016)+2017
m = 1 + ( -2 ) + 3 + ( -4 ) + ....... + ( - 2016 ) + 2017
m = [ 1 + ( - 2 ) ] + [ 3 + ( -4 ) ] + ...... + [ 2015 + ( -2016 ) + 2017
m = ( -1 ) + ( -1 ) + ...... + ( -1 ) + 2017
có 1008 số -1
m = ( -1 ) x 1008 + 2017
m = ( -1008 ) + 2017
, = 1009
Ta có :
m = 1 + ( -2 ) + 3 + ( -4 ) + ....... + ( - 2016 ) + 2017
m = [ 1 + ( - 2 ) ] + [ 3 + ( -4 ) ] + ...... + [ 2015 + ( -2016 ) + 2017
m = ( -1 ) + ( -1 ) + ...... + ( -1 ) + 2017 [ có 1008 số -1 ]
m = ( -1 ) x 1008 + 2017
m = ( -1008 ) + 2017
m = 1009