Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
1/1+2 + 1/1+2+3 +1/1+2+3+4 +...+1/1+2+3+...+50
Ta có 2/2(1+2)+2/2(1+2+3)+...+2/2(1+2+...+50)
=2/6+2/12+2/20+...+2/2550
=2/2.3+2/3.4+...+2/50.51
=2(1/2.3+1/3.4+...+1/50.51)
=2(1/1-1/2+1/2-...+1/50-1/51)
=2.(1-1/51)
=2.50/51=100/51
\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+4+...+50}\)
\(=\frac{1}{2.3:2}+\frac{1}{3.4:2}+\frac{1}{4.5:2}+...+\frac{1}{50.51:2}=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{100.101}\)
\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{50.51}\right)=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{50}-\frac{1}{51}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{51}\right)=\frac{1}{2}.\frac{49}{102}=\frac{49}{204}\)
\(A=\frac{1}{1+2}+\frac{1}{1+2+3}+..+\frac{1}{1+2+3+...+50}\)
Ta có :
\(A=\frac{2}{2\left(1+2\right)}+\frac{2}{2\left(1+2+3\right)}+...+\frac{2}{2\left(1+2+..+50\right)}\)
\(A=\frac{2}{6}+\frac{2}{12}+...+\frac{2}{2550}\)
\(A=\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{50.51}\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{50}-\frac{1}{51}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{51}\right)\)
\(A=2\times\frac{49}{102}\)
\(A=\frac{49}{51}\)
đề bài mk chỉ cho 50 thôi ko có 51 đâu
nên mk cho bạn 1k thôi nhé
Đặt A = 1.2 + 2.3 + 3.4 + ... + 50.51
=> 3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 50.51.3
= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + .... + 50.51.(52 - 49)
= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 50.51.52 - 49.50.51
= 50.51.52
= 132600
Vì 3A = 132600
=> A = 44300
Vậy 1.2 + 2.3 + 3.4 + ... + 50.51 = 44300
A=1+1/2x3+1/3X6+1/4X10+...+1/16X136
A=1+3/2+2+5/2+3+...+17/2
A=2/2+3/2+4/2+5/2+6/2+...+17/2
A=2+3+4+5+...+16+17/2
A=(2+17)x16:2/2
A=19x16:2/2
A=304:2/2
A=152/2
A=76
****
\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+4+...+50}\)
\(=\frac{1}{\left(1+2\right).2:2}+\frac{1}{\left(1+3\right).3:2}+\frac{1}{\left(1+4\right).4:2}+...+\frac{1}{\left(1+50\right).50:2}\)
\(=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{50.51}\)
\(=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{50.51}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{50}-\frac{1}{51}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{51}\right)\)
\(=2.\frac{49}{102}=\frac{49}{51}\)
Ủng hộ mk nha ^_-