=1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16

=1-1/16=15/16

Ta có : \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\)

\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.......+\frac{1}{13}-\frac{1}{16}\)

\(=1-\frac{1}{16}\)

\(=\frac{15}{16}\)

= 15/16

Tk mình nha!

Chúc bạn học giỏi

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Mình cần gấp lắm

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Lời giải:

$M=\frac{4-1}{1\times 4}+\frac{7-4}{4\times 7}+\frac{10-7}{7\times 10}+....+\frac{22-19}{19\times 22}+\frac{25-22}{22\times 25}$

$=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+....+\frac{1}{22}-\frac{1}{25}$

$=1-\frac{1}{25}=\frac{24}{25}$

Ta có :

1/1.4+1/4.7+...+1/91.94

=1/3.(1/1-1/4+...+1/91-1/94)

=1/3.(1/1-1/94)

=1/3.93/94

=31/94

Ta có :

1/1.4+1/4.7+...+1/91.94

=1/3.(1/1-1/4+...+1/91-1/94)

=1/3.(1/1-1/94)

=1/3.93/94

=31/94

\(A=\dfrac{3}{7x10}+\dfrac{3}{10x13}+\dfrac{3}{13x16}+...+\dfrac{3}{97x100}\)

\(A=3x\left(\dfrac{1}{7x10}+\dfrac{1}{10x13}+\dfrac{1}{13x16}+...+\dfrac{1}{97x100}\right)\)

\(A=3x\dfrac{1}{3}x\left(\dfrac{1}{7}-\dfrac{1}{10}+\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)

\(A=3x\dfrac{1}{3}x\left(\dfrac{1}{7}-\dfrac{1}{100}\right)\)

\(A=1x\left(\dfrac{100}{700}-\dfrac{7}{700}\right)=\dfrac{93}{700}\)

\(a,\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+....+\frac{1}{384}\)

\(\text{Đ}\text{ặt}\)\(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+...+\frac{1}{384}\)

\(2A=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+....+\frac{1}{192}\)

\(2A-A=\frac{1}{3}-\frac{1}{384}\)

a đề sai

b)Đặt A=1/4x7 + 1/7x10 + 1/10x13 +...........+ 1/19x22

\(3A=3\left(\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{19.22}\right)\)

\(3A=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{19}-\frac{1}{22}\)

\(3A=\frac{1}{4}-\frac{1}{22}\)

\(A=\frac{9}{44}:3\)

\(A=\frac{3}{44}\)

\(a,\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{43.45}=\frac{5}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{43.45}\right)=\frac{5}{3}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{43}-\frac{1}{45}\right)=\frac{5}{3}.\frac{44}{45}=\frac{44}{27}\)

\(A=\frac{1}{1.4}+\frac{1}{4.7}+.....+\frac{1}{97.100}\)

\(3A=\frac{3}{1.4}+\frac{3}{4.7}+......+\frac{3}{97.100}\)

\(3A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.......+\frac{1}{97}-\frac{1}{100}\)

\(3A=1-\frac{1}{100}\)

\(3A=\frac{99}{100}\)

\(A=\frac{99}{100}:3\)

\(A=\frac{33}{100}\)

A=1/1x4+1/4x7+.....+1/97x100

A=1x3/1x4x3+1x3/4x7x3+....+1x3/97x100x3

A=1/3x(3/1x4+3/4x7+...+3/97x100)

A=1/3x(1-1/4+1/4-1/7+.....+1/97-1/100)

A=1/3x(1-1/100)

A=1/3x99/100

A=33/100

a=511/256

b=647/20

c=mình đang suy nghĩ,nhưng nếu bạn k cho mình thì bạn sẽ có câu trả lời

a. 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256

= 1 + ( 1 - 1/2) + ( 1/2 - 1/4) + ( 1/4 - 1/8) + ( 1/8 - 1/16) + ( 1/16 - 1/32) + (1/32 - 1/64) + ( 1/64 - 1/128) + (1/128 - 1/256)

= 1 + 1 - 1/2 + 1/2 - 1/4 + 1/4 - 1/8 + 1/8 - 1/16 + 1/16 - 1/32 + 1/32 - 1/64 + 1/64 - 1/128 + 1/128 - 1/256

= 2 - 1/256

= 511/256

Câu b bạn có viết sai đề không vậy?