Dat bieu thuc tren la A

2A=10/2.4+10/4.6+10/6.8+...+10/48.50

2A=5.(2/2.4+2/4.6+2/6.8+...+2/48.50)

2A=5.(1/2-1/4+1/4-1/6+1/6-1/8+..+1/48-1/50)

2A=5.(1/2-1/50)

2A=5.12/25

2A=12/5

A=12/5:2

A=12/5.1/2

A=6/5

=  5/2 . ( 1/2 - 1/4 + 1/4 - 1/6 + ...... + 1/48 - 1/50)

= 5/2 . ( 1/2 - 1/50)

= 5/2 . 12.25

=6/5

\(A=\frac{5}{2\times4}+\frac{5}{4\times6}+.....+\frac{5}{48\times50}\)

\(\Rightarrow\frac{2}{5}A=\frac{2}{5}\left(\frac{5}{2\times4}+\frac{5}{4\times6}+.....+\frac{5}{48\times50}\right)\)

\(\Rightarrow\frac{2}{5}A=\frac{2.5}{5.\left(2\times4\right)}+\frac{2.5}{5.\left(4\times6\right)}+.....+\frac{2.5}{5.\left(48\times50\right)}\)

\(\Rightarrow\frac{2}{5}A=\frac{2}{\left(2\times4\right)}+\frac{2}{\left(4\times6\right)}+.....+\frac{2}{\left(48\times50\right)}\)

\(\Rightarrow\frac{2}{5}A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+.....+\frac{1}{48}-\frac{1}{50}\)

\(\Rightarrow\frac{2}{5}A=\frac{1}{2}-\frac{1}{50}\)

\(\Rightarrow\frac{2}{5}A=\frac{24}{50}\)

\(\Rightarrow A=\frac{24}{50}:\frac{2}{5}=\frac{24}{50}\times\frac{5}{2}=\frac{6}{5}\)

Đề yêu cầu gì vậy em?

25C=5^52-5^50+5^48-5^46+...+5^8-5^6+5^4-5^2

=>26C=5^52-1

=>\(C=\dfrac{5^{52}-1}{26}\)

Đề đúng rồi đúng ko em? Nghĩa là 2 số hạng cuối là \(-5^2-1\) chứ không phải \(+5^2-1\)?

\(C=5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4-1\)

\(=5^{48}\left(5^2-1\right)+5^{46}\left(5^2-1\right)+...+5^4\left(5^2-1\right)-5^2-1\)

\(=5^{48}.24+5^{46}.24+...+5^4.24-25-1\)

\(=5^{46}.5^2.24+5^{44}.5^2.24+...+5^2.5^2.24-26\)

\(=5^{46}.600+5^{44}.600+...+5^2.600-100+74\)

\(=100.\left(5^{46}.6+5^{44}.6+...+5^2.6-1\right)+74\)

Vậy C chia 100 dư 74

A = - ( 5 - 6 ) - ( 3 - 4 + 5 - 7 )

A = -5 + 6 - 3 + 4 - 5 + 7

A = ( 6 + 4 ) + ( -5 + (-5) ) + ( -3 + 7 )

A = 10 + (-10) + 4

A = 0 + 4

A = 4

P = ( 1 + 3 + 5 + ... + 47 + 49 ) - ( 2 + 4 + 6 + ... + 48 + 50 )

P = \(\frac{\left(1+49\right)\cdot\left(\left(49-1\right):2+1\right)}{2}\)  -  \(\frac{\left(2+50\right)\cdot\left(\left(50-2\right):2+1\right)}{2}\)

P = \(625-650\)

P = \(-25\)

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