Tính tổng S=9x11+99x101+999x1001+9999x10001+99999x100001
Tính tổng A biết A 2 7x9 2 9x11 2 11x13 ... 2 97x99 2 99x101
Tính nhanh:
(7/5x7)+(7/7x9)+(7/9x11)+...+(7/99x101)
1x3+5x7+9x11+...+99x101
1x3+5x7+9x11+...+99x101
2/7x9+2/9x11+2/11x13+.......+2/97x99+99x101
2/(7 × 9) + 2/(9 × 11) + 2/(11 × 13) + ... + 2/(97 × 99)
= 1/7 - 1/9 + 1/9 - 1/11 + 1/11 - 1/13 + ... + 1/97 - 1/99
= 1/7 - 1/99
= 92/693
Tính:
a) N=1x3+5x7+9x11+...+99x101
b) P=1^2+4^2+7^2+....+100^2
4/5x7+4/7x9+4/9x11+4/11*13.........+4/99x101
/ là dấu gạch ngang giữa phân số
\(\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}+...+\frac{4}{99.101}\)
\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{99.101}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{101}\right)\)
\(=2.\frac{96}{505}\)
\(=\frac{192}{505}\)
4/5x7+4/7x9+4/9x11+4/11*13.........+4/99x101
/ là dấu gạch ngang giữa phân số
\(\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{99.101}\)
\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{101}\right)\)
\(=2.\left(\frac{101}{505}-\frac{5}{505}\right)\)
\(=2.\frac{96}{505}\)
\(=\frac{192}{505}\)
Chúc bạn học tốt !!!
\(B=\frac{4}{3x5}-\frac{6}{5x7}+\frac{8}{7x9}-\frac{10}{9x11}+\frac{12}{11x13}-...+\frac{100}{99x101}\)