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Ta có : C = 1 + 3 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 310 + 311
= (1 + 3 + 32 + 33) + (34 + 35 + 36 + 37) + (38 + 39 + 310 + 311)
= (1 + 3 + 32 + 33) + 34.(1 + 3 + 32 + 33) + 38.(1 + 3 + 32 + 33)
= 40 + 34.40 + 38.40
= 40.(1 + 3 + 32 + 33)
= 10.4.(1 + 3 + 32 + 33) \(⋮\)10
=> \(C⋮10\left(\text{ĐPCM}\right)\)
\(S=6^2\left(1^2+2^2+3^2+...+10^2\right)=36.385=13860\)
Tính:
(-2)2.3 -(110+8):(-3)2
=4.3-(1+8):9
=12-9:9
=12-1
=11
tinh tong cua 11,10,9,8,7,6,5,..........,-37,-38
-675 nha ban
Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100
4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100)4
4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)
4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100
4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101
4A=98.99.100.101
=>A=98.99.100.101/4
=> A=24497550
\(a;5^{23}=5\cdot5^{22}< 6\cdot5^{22}\Rightarrow5^{23}< 6\cdot5^{22}\)
\(b;7\cdot2^{13}< 8\cdot2^{13}=2^3\cdot2^{13}=2^{15}\)
\(c;21^{15}=3^{15}\cdot7^{15}>3^{15}\cdot7^{14}=27^5\cdot49^8\)
\(d;199^{20}< 200^{20}=10^{40}\cdot2^{20}< 10^{45}\cdot2^{15}=2000^{15}< 2001^{15}\)
\(e;3^{39}=9^{13}< 11^{13}< 11^{21}\)
\(C=3^{(10+11+12+...+50)}\)
\(C=3^{1230}\)
\(C=3^{10}+3^{11}+...+3^{50}\)
\(\Rightarrow3C=3^{11}+3^{12}+...+3^{51}\)
\(\Rightarrow3C-C=\left(3^{11}+...+3^{51}\right)-\left(3^{10}+...+5^{50}\right)\)
\(\Rightarrow2C=3^{51}-3^{10}\)
\(\Rightarrow C=\frac{3^{51}-3^{10}}{2}\)