Tính : Q = 1.22 + 2.32 + 3.42 + …+ 19. 202
A=1.22+2.32+3.42+...+2017.20182
D=1.22+2.32+3.42+...........+99.1002
Các số có tổng từ 1->100 có tổng là:2600
Có 200 số 2 nên ta lấy
2600.200=520 000
=>D=520 000
Tính: A = 1.22 + 2.32 + 3.44 + ....+ 2017.20182
Rút gọn phân số sau:
T=1.2.4+2.3.5+3.4.6+...+100.101.103 / 1.12+ 2.32+ 3.42+...+ 100.302
Tính B = \(\frac{\left(3.42^4\right)^2}{5.2^5.4^2-16^2}\)
Thực hiện phép tính:
a) ( 7 . 5 8 – 8 . 5 4 + 12 5 ) : 5 2 ;
b) ( 3 . 4 2 + 8 2 + 3 . 16 2 ) : 2 3 .
Tính A, biết: (tính nhanh, ko tính máy tính)
\(A=\frac{1}{2.32}+\frac{1}{3.33}+\frac{1}{4.34}\)
30A=30/2*32+30/3*33+30/4*34=1/2-1/32+1/3-1/33+1/4-1/34=99/100
A=3,3/100
\(=\frac{1}{30}.\left(\frac{30}{2.32}+\frac{30}{3.33}+\frac{30}{4.34}\right)\)
\(=\frac{1}{30}.\left(\frac{1}{2}-\frac{1}{32}+\frac{1}{3}-\frac{1}{33}+\frac{1}{4}-\frac{1}{34}\right)\)
Tự làm tiếp nhé
Tính P/Q biết:
P = 1/2.32 + 1/3.33 + ... + 1/n.(n+30) + ... + 1/1973.2003
Q = 1/2.1974 + 1/3.1975 + ... + 1/n.(n+1972) + ... + 1/31.2003
\(P=...\)
\(=\frac{1}{30}\left(\frac{30}{2.32}+\frac{30}{3.33}+...+\frac{30}{1973.2003}\right)\)
\(=\frac{1}{30}\left(\frac{1}{2}-\frac{1}{32}+\frac{1}{3}-\frac{1}{33}+...+\frac{1}{1973}-\frac{1}{2003}\right)\)
\(=\frac{1}{30}\left[\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1973}\right)-\left(\frac{1}{32}+\frac{1}{33}+...+\frac{1}{2003}\right)\right]\)
\(=\frac{1}{30}\left[\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{31}\right)-\left(\frac{1}{1974}+\frac{1}{1975}+...+\frac{1}{2003}\right)\right]\)
\(Q=...\)
\(=\frac{1}{1972}\left(\frac{1972}{2.1974}+\frac{1972}{3.1975}+...+\frac{1}{31.2003}\right)\)
\(=\frac{1}{1972}\left(\frac{1}{2}-\frac{1}{1974}+\frac{1}{3}-\frac{1}{1975}+...+\frac{1}{31}-\frac{1}{2003}\right)\)
\(=\frac{1}{1972}\left[\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{31}\right)-\left(\frac{1}{1974}+\frac{1}{1975}+...+\frac{1}{2003}\right)\right]\)
Gọi \(\left[\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{31}\right)-\left(\frac{1}{1974}+\frac{1}{1975}+...+\frac{1}{2003}\right)\right]=A\)
Ta có:\(\frac{P}{Q}=\left(\frac{1}{30}.A\right):\left(\frac{1}{1972}.A\right)=\frac{A}{30}\cdot\frac{1972}{A}=\frac{1972}{30}=\frac{986}{15}\)
tính bằng 2 cách
d. 202 x 19 - 9 x 202
mọi người giúp em nha
d) \(202\times19-9\times202=202\times\left(19-9\right)=202\times10=2020\)
\(202\times19-9\times202=3838-1818=2020\)
202 x 19 - 9 x 202
= 3838 - 1818
= 2020
202 x ( 19-9)
= 202 x 10
= 2020
c1 202 *( 19-9)
= 202*10= 2020
Cách 2 bạn tính bth thui nhân chia trước cộng trừ sau