A=-1275

nhân cả hai vế với 2, lấy 2A-A ra A=4

\(A=\left(1+2+2^2+...+2^{49}\right)-\left(2^{50}+3\right)\)

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

\(2A-A=2+2^3+2^4+...+2^{50}-2\left(2^{50}+3\right)-1-2-2^2-...2^{49}+\left(2^{50}+3\right)\)\(A=2^{50}-3-\left(2^{50}+3\right)\)

\(A=-6\)

-1-2-.....-49-50=-(1+50)-(2+49)-.....-(25+26)=-51-51-.....-51(có 25 số 51)=-51x25=-1275

Ra -1275 

B = ( -1 ) - 2 + ( - 3 ) - 4 + ... + ( - 49 ) - 50 Có 50 số hạng

B =  ( - 3 )  +(  - 7 ) + .... + ( - 99 ) có 50 : 2 = 25 số hạng

Tổng B là  [( - 99 ) + ( - 3 ) ] x 25 : 2 = ( - 1275 )

Vậy B = -1275

-1225 nhé

=1275

đúng thì k nha

A=-(1+2+3+4+...+49+50)

A=-(1275)

=>A=-1275

\(A=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+....+\frac{1}{1+2+3+...+49+50}\)

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

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

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

\(=2\left(\frac{1}{2}-\frac{1}{51}\right)=\frac{49}{51}\)