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\(2C=2+6+12+20+...+2450\)
\(2C=1.2+2.3+3.4+4.5+...+49.50\)
\(6C=1.2.3+2.3.3+3.4.3+...+49.50.3\)\(6C=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+49.50.\left(51-48\right)\)
\(6C=1.2.3+2.3.4-1.2.3+...+49.50.51-49.50.51\)
\(6C=49.50.51\)
\(6C=124950\)
\(C=20825\)
\(C=-\left[\dfrac{1}{3}\cdot\dfrac{\left(3+1\right)\cdot3}{2}+\dfrac{1}{4}\cdot\dfrac{\left(4+1\right)\cdot4}{2}+...+\dfrac{1}{50}\cdot\dfrac{\left(50+1\right)\cdot50}{2}\right]\\ C=-\left(\dfrac{1}{3}\cdot\dfrac{4\cdot3}{2}+\dfrac{1}{4}\cdot\dfrac{5\cdot4}{2}+...+\dfrac{1}{50}\cdot\dfrac{51\cdot50}{2}\right)\\ C=-\left(2+\dfrac{5}{2}+...+\dfrac{51}{2}\right)\\ C=-\dfrac{4+5+...+51}{2}=-\dfrac{\dfrac{\left(51+4\right)\left(51-4+1\right)}{2}}{2}=-\dfrac{55\cdot48}{4}=-660\)
1: =72/90+65/90=137/90
2: =24/56-77/56=-53/56
3: =-7/10+4/5=1/10
4: =15/100-4/100=11/100
5: =4/6-5/6=-1/6
6: =10/40-15/40-76/40=-81/40
7: =-9/10+7/18
=-81/90+35/90=-46/90=-23/45
8: =27/90-55/90=-28/90=-14/45
9: =36/60-50/60-35/60=-49/60
10: =-4/9+5/6-3/8
=-32/72+60/72-27/72
=1/72
\(E=1.2.3+2.3.4+3.4.5+...+18.19.20\)
\(4E=1.2.3.4+2.3.4.4+3.4.5.4+...+18.19.20.4\)
\(4E=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+...+18.19.20.\left(21-17\right)\)
\(4E=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+18.19.20.21-17.18.19.20\)
\(4E=18.19.20.21\)
\(4E=143640\)
\(E=\frac{143640}{4}\)
\(E=35910\)
Chúc bạn học tốt ~
\(G=2.4.6+4.6.8+6.8.10+...+18.20.22\) ( xem lại đề có nhầm dấu ko nha bn )
\(8G=2.4.6.8+4.6.8.8+6.8.10.8+...+18.20.22.8\)
\(8G=2.4.6.8+4.6.8.\left(10-2\right)+6.8.10.\left(12-4\right)+...+18.20.22\left(24-16\right)\)
\(8G=2.4.6.8+4.6.8.10-2.4.6.8+6.8.10.12-4.6.8.10+...+18.20.22.24-16.18.20.22\)
\(8G=18.20.22.24\)
\(8G=190080\)
\(G=\frac{190080}{8}\)
\(G=23760\)
Chúc bạn học tốt ~
C = 13 + 23 + 33 + 43 + ..... + 103
\(C = 1 + 8+ 27+ 64 + 125 + 216 +343 +512 +729+ 1000 = 4025\)
~~~học tốt nha~~~
\(C=1^3+2^3+...+10^3=\frac{2^3\left(1^3+2^3+...+10^3\right)}{2^3}=\frac{2^3+4^3+...+20^3}{8}=\frac{24200}{8}=3025\)