Question

tính hợp lí

a) 1+6+11+16+.......+46+51

b) \(\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}+\frac{5^2}{26.31}\)

Answer 1

a) áp dụng dãy số cách đều đi

Answer 2

a, 1+6+11+16+...+46+51

Số số hạng là : (51-1):5+1 = 11 ( số )

Tổng là : (51+1).11:2=286

b, Đặt A = \(\dfrac{5^2}{1.6}+\dfrac{5^2}{6.11}+\dfrac{5^2}{11.16}+\dfrac{5^2}{16.21}+\dfrac{5^2}{21.26}+\dfrac{5^2}{26.31 } \)

\(\dfrac{1}{5}A=\) \(\dfrac{5}{1.6}+\dfrac{5}{6.11}+\dfrac{5}{11.16}+\dfrac{5}{16.21}+\dfrac{5}{21.26}+\dfrac{5}{26.31}\)

\(\dfrac{1}{5}A=\) \(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{31}\)

\(\dfrac{1}{5}A=1-\dfrac{1}{31}\)

\(\dfrac{1}{5}A=\dfrac{30}{31}\)

\(A=\dfrac{30}{31}:\dfrac{1}{5}=\dfrac{150}{31}\)

Vậy..