2⁵⁰-2⁴⁹-2⁴⁸-..........-2²-2

=2.(1⁵⁰-1⁴⁹-................-1²-1)

=2.(-50)

=-100

\(B=2^{50}-2^{49}-2^{48}-2^{47}-...-2^2-2\)

Đặt \(A=2^{49}+2^{48}+...+2\)

\(\Rightarrow2A=2^{50}+2^{49}+...+2^2\)

\(\Rightarrow A=2A-A=2^{50}+2^{49}+...+2^2-2^{49}-2^{48}-...-2=2^{50}-2\)

\(\Rightarrow B=2^{50}-A=2^{50}-2^{50}+2=2\)

đơn giản thôi

\(A=\frac{2}{2\cdot3\cdot4}+\frac{2}{3\cdot4\cdot5}+...+\frac{2}{47\cdot48\cdot49}+\frac{2}{48\cdot49\cdot50}\)

\(A=\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+...+\frac{1}{47\cdot48}-\frac{1}{48\cdot49}+\frac{1}{48\cdot49}-\frac{1}{49\cdot50}\)

\(A=\frac{1}{2\cdot3}-\frac{1}{49\cdot50}\)

\(A=\frac{1}{6}-\frac{1}{2450}\)

\(A=\frac{611}{3675}\)

mong giúp đc bn.thk cho mk 

sai bet

1+12=13

giup mih voi

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

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

\(50^2-49^2+48^2-47^2+...+2^2-1\)

\(=\left(50-49\right)\left(50+49\right)+\left(48-47\right)\left(48-47\right)+...+\left(2-1\right)\left(2+1\right)\)

\(=99+95+...+3\)

\(=\frac{\left(99+3\right)\left[\left(99-3\right):4+1\right]}{2}\)

\(=\frac{102.\left(24+1\right)}{2}=\frac{102.25}{2}=1275\)