Question

 

Em tick cho giúp em với em cần gấp lắm

D=1*2+2*3+3*4+4*5+............+99*100+100*101

E=2+2^3+2^5+2^7+............+2^2017+2^2019

 

Answer 1

D = 1 . 2 + 2 . 3 + 3 . 4 + 4 . 5 + .... + 99 . 100 + 100 . 101

3D=1 . 2 . 3 + 2 . 3 . ( 4 - 1 ) + 3 . 4 . ( 5 - 2 )+ 4 . 5 + ( 6 - 3) + .... + 99. 100 . ( 101 - 98 ) + 100 . 101 . ( 102 - 99 )

3D=1 . 2 . 3+2 . 3 . 4-1 . 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + 4 . 5 . 6 - 3 . 4  . 5 + ..... + 99 . 100 . 101- 98 . 99 . 100 +100 . 101 . 102-99.100.101

3D = 100 . 101 . 102 

D = \(\frac{100.101.102}{3}=343400\)

E = \(2+2^3+2^5+2^7+...+2^{2017}+2^{2019}\)

4E = \(2^3+2^5+2^7+2^9...+2^{2019}+2^{2021}\)

=> 4E - E = \(2^3+2^5+2^7+2^9...+2^{2019}+2^{2021}\)- ( \(2+2^3+2^5+2^7+...+2^{2017}+2^{2019}\))

=> 3E = \(2^{2021}-2\)

=> E = \(\frac{2^{2021}-2}{3}\)