a,  2 17 + 17 2 9 15 - 3 15 2 4 - 4 2

=  2 17 + 17 2 9 15 - 3 15 16 - 16

=  2 17 + 17 2 9 15 - 3 15 . 0

= 0

b,  1 2 + 2 3 + 3 4 + 4 5 . ( 1 3 + 2 3 + 3 3 + 4 3 ) ( 3 8 - 81 2 )

=  1 2 + 2 3 + 3 4 + 4 5 . ( 1 3 + 2 3 + 3 3 + 4 3 ) ( 3 4 . 2 - 81 2 )

=  1 2 + 2 3 + 3 4 + 4 5 . ( 1 3 + 2 3 + 3 3 + 4 3 ) ( 81 2 - 81 2 )

=  1 2 + 2 3 + 3 4 + 4 5 . ( 1 3 + 2 3 + 3 3 + 4 3 ) . 0

= 0

c,  7 24 + 7 23 : 7 22

=  7 24 : 7 22 + 7 23 : 7 22

=  7 24 - 22 + 7 23 - 22

=  7 2 + 7 1

= 49 + 7 = 56

a: Ta có: \(\left(2^{17}+17^2\right)\cdot\left(9^{15}-3^{15}\right)\cdot\left(2^4-4^2\right)\)

\(=\left(2^{17}+17^2\right)\cdot\left(9^{15}-3^{15}\right)\cdot\left(16-16\right)\)

=0

b: Ta có: \(\dfrac{8^{2017}-8^{2015}}{8^{2104}\cdot8}\)

\(=\dfrac{8^{2015}\cdot\left(8^2-1\right)}{8^{2105}}\)

\(=\dfrac{1\cdot63}{8^{90}}\)+

c: Ta có: \(\left(1^3+2^3+3^4+4^5\right)\cdot\left(1^3+2^3+3^3+4^3\right)\cdot\left(3^8-81^2\right)\)

\(=\left(1^3+2^3+3^4+4^5\right)\cdot\left(1^3+2^3+3^3+4^3\right)\cdot\left(3^8-3^8\right)\)

=0

d: Ta có: \(\left(2^8+8^3\right):\left(2^5\cdot2^3\right)\)

\(=\dfrac{2^8+2^9}{2^8}\)

=3

\(\left(2^{17}+7^2\right).\left(9^{15}-3^{15}\right).\left(2^4-4^2\right)\)

\(=\left(2^{17}+7^2\right).\left(9^{15}-3^{15}\right).\left(16-16\right)\)

\(=\left(2^{17}+7^2\right).\left(9^{15}-3^{15}\right).0\)

\(=0\)

-------------------------------------------------

\(\left(7^{1997}-7^{1995}\right):\left(7^{1994}.7\right)\)

\(=\left[7^{1995}\left(7^2-1\right)\right]:7^{1995}\)

\(=7^{1995}.48:7^{1995}\)

\(=48\)

-------------------------------------------------

\(\left(1^2+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).\left(3^8-81^2\right)\)

\(=\left(1^2+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).\left(6561-6561\right)\)

\(=\left(1^2+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).0\)

\(=0\)

-------------------------------------------------

\(\left(2^8+8^3\right):\left(2^5.2^3\right)\)

\(=\left[2^8+\left(2^3\right)^3\right]:2^8\)

\(=\left(2^8+2^9\right):2^8\)

\(=2^8.\left(1+2\right):2^8\)

\(=2^8.3:2^8\)

\(=3\)

sos

\((2^{17}+17^{2}).(9^{15}-3^{15}).(2^{4}-4^{2})\)

\(=(2^{17}+17^{2}).(9^{15}-3^{15}).(16-16)\)

\(=(2^{17}+17^{2}).(9^{15}-3^{15}).0\)

\(=0\)

\((7^{1997}-7^{1995}):(7^{1994}.7)\)

\(=(7^{1997}-7^{1995}):7^{1995}\)

\(=7^{1997}:7^{1995}-7^{1995}:7^{1995}\)

\(=7^{2}-1=49-1=48\)

\(1^{2}+2^{3}+3^{4}+4^{5}).(1^{3}+2^{3}+3^{3}+4^{3}).(3^{8}-81^{2})\)

\(=(1^{2}+2^{3}+3^{4}+4^{5}).(1^{3}+2^{3}+3^{3}+4^{3}).(6561-6561)\)

\(=(1^{2}+2^{3}+3^{4}+4^{5}).(1^{3}+2^{3}+3^{3}+4^{3}).0\)

\(=0\)

\((2^{8}+8^{3}):(2^{5}.2^{3})\)

\(=[2^{8}+(2^{3})^{3}]:2^{8}\)

\(=(2^{8}+2^{9}):2^{8}\)

\(=2^{8}:2^{8}+2^{9}:2^{8}\)

\(=1+2=3\)

Hướng dẫn giải:

áp dụng kiến thức tính nhanh ý

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50=1275

= 1275

=1275

=1245

Có ai rảnh đâu mà đi ngồi cộng ngần đấy số ra.

=1275

1 + 2 + 3 +...+ 50

Dãy trên có số số hạng là:

\(\left(50-1\right)+1=50\) (số)

Tổng của chúng là:

\(\frac{\left(50+1\right)\cdot50}{2}=1275\)

Vậy tổng của chúng là 1275

~Học tốt~

Kết quả :

= 1275

Hk tốt nha bn !