=> A = 1 x 50 + 2 x ( 50 - 1 ) + 3 x ( 50 - 2 ) + .... + 49 x ( 50 - 48 ) + 50 x ( 50 - 49 )

         = 1 x 50 + 2 x 50 - 1 x 2 + 3 x 50 - 2 x 3 + ..... + 49 x 50 - 48 x 49 + 50 x 50 - 49 x 50

         = ( 1 + 2 + 3 + .... + 50 ) x 50 + ( 1 x 2 + 2x 3 + .... + 49 x 50 )

         = \(\frac{50.\left(50+1\right)}{2}\times50+\frac{49.50.51}{3}\)

         = 63750 + 41650

        = 105400

So sánh tổng : S = 1/5 + 1/9 + 1/10 + 1/41 + 1/42 với 1/2

S=

=50/50+50/49+50/48+...+50/2

=50.(1/50+1/49+1/48+...+1/4+1/3+1/2)

=50

P=

P=(1/49+1)+(2/48+1)+...+(48/2+1)+1

P= 50/49+50/48+....+50/2+50/50=1

vậy s/p = 1/50

P = 1/49+2/48+3/47+...+48/2+49/1

Cộng 1 váo mỗi p/s trong 48 p/s đầu , trừ p/s cuối đi 48 ta đượ

P=(1/49+1)+(2/48+1)+...+(48/2+1)+1

P= 50/49+50/48+....+50/2+50/50

Đưa ps cuối lên đầu

P=50/50+50/49+50/48+...+50/2

=50.(1/50+1/49+1/48+...+1/4+1/3+1/2)

=50.S

VậyS/P=1/50
 

1/50

 chúc bạn học tốt :-)))

SAI CHÍNH TẢ QUÁ NHIỀU

\(\dfrac{1}{50}-\dfrac{1}{50.49}-\dfrac{1}{49.48}-...-\dfrac{1}{2.1}\\ =-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{48.49}+\dfrac{1}{49.50}-\dfrac{1}{50}\right)\\ =-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{48}-\dfrac{1}{49}+\dfrac{1}{49}-\dfrac{1}{50}-\dfrac{1}{50}\right)\\ =-\left(1-\dfrac{1}{50}-\dfrac{1}{50}\right)\\ =-\dfrac{24}{25}\)

A = 1 × 2 × 3 + 2 × 3 × 4 + .....+ 48 × 49 × 50

ta có 4 x A = 1 x 2 x 3 x 4 + 2 x 3 x 4 x (5 -1) + .....+ 48 × 49 × 50 x (51 - 47)

= 1 x 2 x 3 x 4 +  2 x 3 x 4 x 5 - 1 x 2 x 3 x 4 + ... + 48 x 49 x 50 x 51 - 47 x 48 x 49 x 50

= 48 x 49 x 50 x 51

suy ra A = (48 x 49 x 50 x 51) : 4

              = 12 x 49 x 50 x 51

nhớ k cho mik nha rùi mik lm nốt cho

A = 1 × 2 × 3 + 2 × 3 × 4 + .....+ 48 × 49 × 50

ta có 4 x A = 1 x 2 x 3 x 4 + 2 x 3 x 4 x (5 -1) + .....+ 48 × 49 × 50 x (51 - 47)

= 1 x 2 x 3 x 4 +  2 x 3 x 4 x 5 - 1 x 2 x 3 x 4 + ... + 48 x 49 x 50 x 51 - 47 x 48 x 49 x 50

= 48 x 49 x 50 x 51

suy ra A = (48 x 49 x 50 x 51) : 4

              = 12 x 49 x 50 x 51