\(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{10}\right).\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{780}\right).a=1\)

=> \(\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{779}{780}.a=1\)

=> \(\frac{4}{6}.\frac{10}{12}.\frac{18}{20}.\frac{28}{30}...\frac{1558}{1560}.a=1\)

=> \(\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}.\frac{4.7}{5.6}...\frac{38.41}{39.40}.a=1\)

=> \(\frac{1.2.3.4...38}{2.3.4.5...39}.\frac{4.5.6.7...41}{3.4.5.6...40}.a=1\)

=> \(\frac{1}{39}.\frac{41}{3}.a=1\)

=> \(\frac{41}{117}.a=1\)

=> \(a=1:\frac{41}{117}=\frac{117}{41}\)

117/41

4949/19800

Ta có A = \(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{10}\right)...\left(1-\frac{1}{780}\right)\)

= \(\frac{2}{3}.\frac{5}{6}.\frac{9}{10}...\frac{779}{780}=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}...\frac{1558}{1560}=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{38.41}{39.40}=\frac{\left(1.2.3...38\right).\left(4.5.6...41\right)}{\left(2.3.4...39\right).\left(3.4.5...40\right)}\)

= \(\frac{1.41}{39.3}=\frac{41}{117}\)

rhsdhtdjdr dryh ry mnse xnyh

g

(1-1/3).(1-1/6).(1-1/10)...(1-1/780) (ko có dấu "...") 
Giải: (1-1/3).(1-1/6).(1-1/10)...(1-1/780) 
= 2/3 . 5/6....779/780 
= 4/6 . 10/12.....1558/1560 
= 1.4 . 2.5 .... 38.41/ 2.3 . 3. 4. .....39.40 
= ( 1.2.3....38).(4.5....41)/(2.3.4....39)(3... 
triệt tiêu xong còn 41/39.3= 41/117 
ĐS = 41/117

1) 6

Tớ chỉ biết thế thui!

a) (3x-4).(X-1)=0

=>3x-4=0 hoặc x-1=0

=>x=4/3 hoặc x=1

b) 2^2X-1.4=8

=>2^2x-1=2¹

=>2x-1=1

=>2x=2

=>x=1

c)Đặt A=1+2+3+......+X

Tổng A có số số hạng là:

(x-1):1+1=x (số)

Tổng A là:

(x+1)*x:2=\(\frac{x^2+x}{2}\)

Thay A vào ta được:\(\frac{x^2+x}{2}=78\)

=>x²+x=156

=>x²+x-156=0

=>x²-12x+13x-156=0

=>x(x-12)+13(x-12)=0

=>(x+13)(x-12)=0

=>\(\orbr{\begin{cases}x=-13\left(loai\right)\\x=12\left(tm\right)\end{cases}}\)

d)(X+1)²=(X+1)⁰

=>(x+1)²=1

=>x²+2x+1-1=0

=>x²+2x=0

=>x(x+2)=0

=>x=0 hoặc x+2=0

=>x=0 hoặc x=-2

e)(2+X)+(4+X)+(6+X)+........+(52+X)=780

=>(2+4+...+52)+(x+x+...+x)=780

=>702+26x=780

=>26x=78

=>x=3