Các bạn trình bày rõ ràng cho mình nha!
A= 3/4 x 8/9 x 15/16 x...x99/100 x 120/121
A=3x8x15x...x99x121/4x9x16x...x100x121
A= 1 x 3 x 2 x 4 x 3 x 5 x ... x 9 x 11 x 10 x 12/ 2 x 2 x 3 x 3 x 4 x 4 x ... x 10 x 10 x 11 x 11
A= (1x2x3x...x9x10)x(3x4x5x...x11x12)/(2x3x4x...x10x11)x(2x3x4x...x10x11)
A=1x12/11x2
A=6/11
Vậy A=6/11
mk trình bày lại:
\(A=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)+...+\left(1-\frac{1}{121}\right)\)
\(=\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)....\left(1-\frac{1}{11^2}\right)\)
\(=\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.\frac{4^2-1}{4^2}......\frac{11^2-1}{11^2}\)
\(=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}.....\frac{10.12}{11^2}\)
\(=\frac{1.2.3.....10}{2.3.4....11}.\frac{3.4.5....12}{2.3.4....11}\)
\(=\frac{1}{11}.\frac{12}{2}=\frac{6}{11}\)
=3/4x4/5x5/6x...x120/121
=3x4x5x6x7x8x9x10x...x120/4x5x6x...x121
=3/121
