D= 3/1.3+3/3.5+....................................+3/49.51
3/1.3 + 3/3.5 + 3/5.7 +...+ 3/49.51
\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{49.51}\)
\(=\frac{2}{3}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right)\)
\(=\frac{2}{3}.\left(1-\frac{1}{51}\right)\)
\(=\frac{2}{3}.\frac{50}{51}=\frac{20}{51}\)
Ủng hộ mk nha !!! ^_^
25/17 mới đúng
3/1.3 + 3/3.5 + 3/5.7 + ... +3/49.51
3/1.3 + 3/3.5 + 3/5.7 + ....... + 3/49.51
= 3 x ( 1/1.3 + 1/3.5 + 1/5.7 + .... + 1/49.51 )
= 3 x ( 1 - 1/51 )
= 3 x 50/51
= 150/151
\(A=\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{49.51}\)
\(A=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{49.51}\right)\)
\(A=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right)\)
\(A=\frac{3}{2}\left(1-\frac{1}{51}\right)\)
\(A=\frac{3}{2}.\frac{50}{51}=\frac{25}{17}\)
Tính nhanh: 3/1.3 + 3/3.5+3/5.7+...+3/49.51
3.2/1.3.2+3.2/3.5.2+3.2/5.7.2+...+3.2/49.51
3/2(2/1.3+2/3.5+2/5.7+....+2/49.51)
3/2(1-1/3+1/3-1/5+1/5-1/7+....+1/49-1/51)
3/2(1-1/51)
3/2 . 50/51
25/17
áp dụng công thức nếu có thừa số thứ 2 ở mẫu trừ đi thừa số thứ 1 bằng số trên tử thi \(\frac{1}{a}-\frac{1}{b}\) ab ở đây là 2 thừa số ở mẫu
VD;3/1.3+3/3.5+...+3/49.51(vì tất cả mẫu trừ cho nhau đều =tử)
nên = 1/1-1/3+1/3+1/5+...+1/49-1/51
=1-1/51
=50/51
tính E= 1.3*3 + 3.5*3 + ...+49.51*3
A=1.3^3+3.5^3-5.7^3+...+49.51^3. Tính tổng A
Tính tổng: 1.3^3 + 3.5^3 +5.7^3+...+49.51^3 ( ^ kí hiệu mũ)
A=\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{3.5}\)+....+\(\frac{3}{49.51}\)
Tính 3/1.3 +3/2.4 +3/3.5 +.....+3/49.51 . Giúp mk với ,mình đang cần gấp
Tính:
a) C = 3/1.3 + 3/3.5 + 3/3.7 +...+ 3/49.51
b) D = 1/2 + 1/14 + 1/35 + 1/65 + 1/104 + 1/152
a; C = \(\dfrac{3}{1.3}\) + \(\dfrac{3}{3.5}\) + \(\dfrac{3}{3.7}\) + ... + \(\dfrac{3}{49.51}\)
C = \(\dfrac{3}{2}\).(\(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + ... + \(\dfrac{2}{49.51}\))
C = \(\dfrac{3}{2}\).(\(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) + ... + \(\dfrac{1}{49}\) - \(\dfrac{1}{51}\))
C = \(\dfrac{3}{2}\).(\(\dfrac{1}{1}\) - \(\dfrac{1}{51}\))
C = \(\dfrac{3}{2}\).\(\dfrac{50}{51}\)
C = \(\dfrac{25}{17}\)