=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

1/1.4+1/4.7+1/7.10+1/10.13+1/13.16

=1/3.(3/1.4+3/4.7+3/7.10+3/10.13+3/13.16)

=1/3.(1/1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+1/13-1/16)

=1/3.(1/1-1/16)

=1/3.(16/16-1/16)=1/3.15/16=5/16

câu a 

quá dễ

3/(1×4)+3/(4×7)+3/(7×10)+3/(10×13)+3/(13×16)

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

=1-1/16

=15/16

31 x 434 x 737 x 10310 x 13 = 1.3289876e+12

mik phải dùng máy tính chứ có sịp nhân mới trả lời đc 

nhỉ ?????

ko có 3/13x16 nha bn

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

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

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

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

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

A= 1/7 - 1/10 + 1/10 - 1/13 + 1/13 - 1/16 + .... + 1/97 - 1/100

A= 1/7 - 1/100

A= 93/700

\(A=\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+...+\frac{3}{97.100}\)

\(A=\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}+...+\frac{1}{37}-\frac{1}{100}\)

\(A=\frac{1}{7}-\frac{1}{100}\)

\(A=\frac{93}{700}\)

Xin lỗi, mình nhầm. Phải bằng 97/700 mới đúng

S = 3/1x4 + 3/4x7 +...+ 3/10x13 + 3/13x16

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

S = 1 + (-1/4 + 1/4) + (-1/7 + 1/7) +...+ (-1/10 + 1/10) + (-1/13 + 1/13) - 1/16

S = 1 +         0         +         0        +...+            0          +           0           - 1/16

S = 1 - 1/16

S = 16/16 - 1/16

S = 15/16

So sánh: 15/16 với 1

vì 15<16

nên 15/16<1

vậy tổng S < 1

3S=1/3(1/1 - 1/4 + 1/4 - 1/7+...+1/13 - 1/16)

3S=1/3(1/1 - 1/16)

3S=1/3 x 15/16

  S=15/16