Question

Tính \(A=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+....+\frac{1}{1+2+3+4+...+50}\)

ai nhanh mk k cho 2 cái luôn

 

Answer 1

\(A=\frac{1}{1+2}+\frac{1}{1+2+3}+..+\frac{1}{1+2+3+...+50}\)

Ta có :

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

\(A=\frac{2}{6}+\frac{2}{12}+...+\frac{2}{2550}\)

\(A=\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{50.51}\)

\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{50}-\frac{1}{51}\right)\)

\(A=2\left(\frac{1}{2}-\frac{1}{51}\right)\)

\(A=2\times\frac{49}{102}\)

\(A=\frac{49}{51}\)

Answer 2

đề bài mk chỉ cho 50 thôi ko có 51 đâu

nên mk cho bạn 1k thôi nhé

Answer 3

Ta có 2/2(1+2) + 2/2(1+2 +3 ) +............+2/2(1+2+3+4+.........+50)

=2/6 + 2/12 + 2/20 +......+2/2550

=2/2x3 + 2/3x 4 + ....+2/50x51

=2(1/2x3 + 1/3x4 + .......1/50 x 51 )

= 2( 1-1/2+1/2-1/3+.....+1/50-1/51)

=2( 1-1/51)

=2 x 50/51

=100/51

MK NHANH NÈ ỦNG HỘ ĐI

Answer 4

A=\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+4+...+50}\)

Ta có:\(\frac{2}{2}.\left(1+2\right)+\frac{2}{2}.\left(1+2+3\right)+\frac{2}{2}.\left(1+2+3+...+50\right)\)

A=\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{2550}\)

A=\(\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{50.51}\)

A=2(\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{50.51}\))

A=\(2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{50}-\frac{1}{51}\right)\)

A=\(2\left(\frac{1}{2}-\frac{1}{51}\right)\)

A=2.\(\frac{49}{102}\)

A=\(\frac{49}{51}\)

Answer 5

A= 49/51

Answer 6

Vậy A = \(\frac{49}{51}\)

Chúc bn hok tốt

Bn nào thấy đùng thì tk mk nhé