tính A= 1.3^3+3.5^3+5.7^3+...+61.63^3
1.3+3.5+5.7+....+61.63
Ta đặt
\(A=1\times3+3\times5+...+61\times63\)
\(6A=1\times3\times6+3\times5\times6+....+61\times63\times6\)
\(6A=1\times3\times6+3\times5\times\left(7-1\right)+...+61\times63\times\left(65-59\right)\)
\(6A=1\times3\times6+3\times5\times7-1\times3\times5+...+61\times63\times65-59\times61\times63\)
\(6A=1\times3\times6-1\times3\times5+61\times63\times65\)
\(6A=3+61\times63\times65\)
\(6A=3\times\left(1+61\times21\times65\right)\)
\(2A=83266\)
\(A=83266\div2=41633\)
3/3.5+3/5.7+...+3/61.63
=3.2/1.3.2+3.2/3.5.2+...+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+...+1/49-1/51)
=3/2.(1-1/51)
=3/2.50/51
=25/17
CHÚC BẠN HỌC GIỎI
K MÌNH NHÉ
A=3/2(2/3.5+2/5.7+...+2/61.63)
=3/2(1/3-1/5+1/5-1/7+...+1/61-1/63)= 3/2(1/3-1/63)=3/2 x 20/63=10/21
Đs: 10/21
\(\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{61.63}\)
\(=3\left(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{61.63}\right)\)
\(=3.\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{61}-\frac{1}{63}\right)\)
\(=\frac{3}{2}\left(\frac{1}{3}-\frac{1}{63}\right)\)
\(=\frac{10}{21}\)
A=1.3^3+3.5^3-5.7^3+...+49.51^3. Tính tổng A
tính A=1.3^3+3.5^3+5.7^3+...+ n.(n+2)^3
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 tổng: 1.3^3 + 3.5^3 +5.7^3+...+49.51^3 ( ^ kí hiệu mũ)
A=3/1.3+3/3.5+3/5.7+...+3/2001.2003
Nhanh lên mình đang cần gấp lắm
Gấp lắm hả :V
\(A=\frac{3}{1\cdot3}+\frac{3}{3\cdot5}+\frac{3}{5\cdot7}+....+\frac{3}{2001\cdot2003}\)
\(=\frac{3}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.....+\frac{1}{2001}-\frac{1}{2003}\right)\)
\(=\frac{3}{2}\left(1-\frac{1}{2003}\right)=\frac{6006}{4006}\)
Tính: A=1.33+3.53+5.73+...+49.513
tính nhanh
\(A=\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{49.51}\)
\(A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{49}-\frac{1}{51}\)
\(A=1-\frac{1}{51}\)
\(A=\frac{50}{51}\)
\(A=\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{49.51}\)
\(2A=3\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\right)\)
\(2A=3\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right)\)
\(2A=3\left(1-\frac{1}{51}\right)\)
\(2A=3.\frac{50}{51}\)
\(2A=\frac{50}{17}\Rightarrow A=\frac{25}{17}\)'