a) \(\frac{13}{7}-\frac{1}{2}\times\frac{13}{7}+\frac{3}{2}\times\frac{13}{7}\)

\(=\frac{13}{7}\times\left(1-\frac{1}{2}+\frac{3}{2}\right)\)

\(=\frac{13}{7}\times2\)

\(=\frac{26}{7}\)

b) \(\frac{1}{15}\times\left(\frac{3}{7}+\frac{5}{19}\right)+\frac{3}{7}\times\left(\frac{5}{19}-\frac{1}{15}\right)\)

\(=\frac{1}{15}\times\frac{3}{7}+\frac{1}{15}\times\frac{5}{19}+\frac{3}{7}\times\frac{5}{19}-\frac{3}{7}\times\frac{1}{15}\)

\(=\frac{5}{19}\times\left(\frac{1}{15}+\frac{3}{7}\right)\)

\(=\frac{5}{19}\times\frac{52}{105}\)

\(=\frac{52}{399}\)

c) \(\frac{5}{6}+\frac{5}{12}+\frac{5}{20}+\frac{5}{30}+...+\frac{5}{9900}\)

\(=5\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{99\times100}\right)\)

\(=5\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(=5\times\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=5\times\frac{49}{100}\)

\(=\frac{49}{20}\)

Lần sau nên đăng ít thôi

A = 5 x (\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+....+\frac{1}{9900}\))

A = 5 x ( \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{99}-\frac{1}{100}\))

A = 5x( \(\frac{1}{2}-\frac{1}{100}\))

A = \(\frac{49}{20}\)

Gọi tổng trên là A

\(\Leftrightarrow A=5\times\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\right)\)

(Tính dãy trong ngoặc) Gọi dãy trong ngoặc là B

\(\Leftrightarrow2B=\frac{1}{3}+\frac{1}{6}+...+\frac{1}{4950}\)

\(\Leftrightarrow2B-B=\left(\frac{1}{3}+\frac{1}{6}+...+\frac{1}{4950}\right)-\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\right)\)

\(\Leftrightarrow B=\frac{1}{3}-\frac{1}{9900}+0+...+0\)

\(\Leftrightarrow B=\frac{3299}{9900}\)

\(\Rightarrow A=5\times\frac{3299}{9900}\)

\(\Rightarrow A=1,6661616...\approx1,7\)

=5/2 x 3 + 5/3x4 + 5/4 x5 + 5/5 x6 + ....... + 5/99 x 100

= 5 x ( 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 +...........+ 1/99 - 1/100)

= 5 x ( 1/2 - 1/100)

= 5 x 49/100

= 49/20

A=3/2+13/12+31/30+...+9901/9900
= 1+1/2+1+1/12+1+1/30+...+1+1/9900
=1+1+1+...+1+1(50 cs)+1/2+1/12+1/30+...+1/9900
=50+1/2+1/12+1/30+...+1/9900
B=5/6+19/20+41/42+...+10099/10100
=(1-1/6)+(1-1/20)+(1-1/42)+...+(1-1/10100)
=1+1+...+1(50cs)-1/6-1/20-1/42-...-1/10100
A-B=(50+1/2+1/12+1/30+...+1/9900)-(50-1/6-1/20-1/42-...-1/10100)
=1/2+1/6+1/12+1/20+...+1/9900+1/10100
=1/1.2+1/2.3+1/3.4+1/4.5+...+1/99.100+1/100.101
=1-1/2+1/2-1/3+1/3-1/4+1/4-...+1/99-1/100+1/100-1/101
=1-1/101
=100/101

cách bạn làm hay đấy

1/2 + 5/6 + 11/12 + 19/20 + 29/30 +. . . 9701 + / 9702 + 9899/9900 = 1/2 + (1-1 / 6) + (1-1 / 12) + (1-1 / 20) + (1-1 / 30) + ...... + (1 -1/9702) + (1-1 / 9900) = 1/2 + [1 - (1 / 2-1 / 3)] + [1 - (1 / 3-1 / 4)] + [1- ( 1 / 4-1 / 5)] + [1 - (1 / 5-1 / 6)] + ...... + [1- (1 / 98-1 / 99)] + [1 - (1 / 99-1 / 100)] * 100 + 1 = 1 / 2-1 / 2 + 1 / 3-1 / 3 + 1 / 4-1 / 4 + 1 / 5-1 / 5 + 1 / 6-1 / 6 + ... ... 1 / 98-1 / 98 + 1 / 99-1 / 99 + 1/100 + 1 = 100/100 = 100 và 1/100

A:tính số số hạng (100 số).

=>A=(1+100)*100:2=5050.

B=1/1*2+1/2*3+1/3*4+000+1/99*100.

=>B=1-1/2+1/2-1/3+1/3-1/4+...+1/99-1/100.

=>B=1-1/100=99/100.

tk mk nha.đúng 1000% .

-chúc ai tk cho mk học giỏi và may mắn,thanks các bn nhìu-

a=100(100+1)/2

B=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100

B=1-1/100=99/100

a= 10000;b=

Câu A tự làm nhé! Tính số số hạng rồi tính tổng

B = 1/1.2 + 1/2.3 + 1/3.4 +.....+ 1/99.100

B = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +........+ 1/99 - 1/100

B = 1 - 1/100

B = 99/100

mk lam dc ma ko ranh ghi

ai giup minh voi

1/2 + 5/6 + 11/12 + 19/20 + 29/30 +. . . 9701 + / 9702 + 9899/9900 = 1/2 + (1-1 / 6) + (1-1 / 12) + (1-1 / 20) + (1-1 / 30) + ...... + (1 -1/9702) + (1-1 / 9900) = 1/2 + [1 - (1 / 2-1 / 3)] + [1 - (1 / 3-1 / 4)] + [1- ( 1 / 4-1 / 5)] + [1 - (1 / 5-1 / 6)] + ...... + [1- (1 / 98-1 / 99)] + [1 - (1 / 99-1 / 100)] * 100 + 1 = 1 / 2-1 / 2 + 1 / 3-1 / 3 + 1 / 4-1 / 4 + 1 / 5-1 / 5 + 1 / 6-1 / 6 + ... ... 1 / 98-1 / 98 + 1 / 99-1 / 99 + 1/100 + 1 = 100/100 = 100 và 1/100