Question

A=2/1*2+2/2*3+2/3*4+...+2/20*21

 

Answer 1

Ta co :

2/( 1*2) + 2/(2*3) + 2/(3*4) + ... + 2/(20*21)

= 2 * ( 1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(20*21) )

= 2 * ( 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/20 - 1/21 )

= 2 * ( 1 - 1/21 )

= 2 * 20/21

= 40 / 21

Answer 2

2/( 1*2) + 2/(2*3) + 2/(3*4) + ... + 2/(20*21)

= 2 * ( 1/(1*2) + 1/(2*3) + 1/(3*4) + ... + 1/(20*21) )

= 2 * ( 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/20 - 1/21 )

= 2 * ( 1 - 1/21 )

= 2 * 20/21

=  \(\frac{40}{21}\)