\(a=\frac{2.9.8+3.12.10+4.15.12+.......+98.297.200}{2.3.4+3.4.5+4.5.6+.........+98.99.100}\)

\(a=\frac{2.\left(3.3\right).\left(4.2\right)+3.\left(4.3\right).\left(5.2\right)+..........+98.\left(99.3\right).\left(100.2\right)}{2.3.4+3.4.5+4.5.6+.................+98.99.100}\)

\(a=\frac{2.3.4.\left(3.2\right)+3.4.5.\left(3.2\right)+............+98.99.100.\left(3.2\right)}{2.3.4+3.4.5+........+98.99.100}\)

\(a=\frac{\left(3.2\right).\left(2.3.4+3.4.5+4.5.6+...........+98.99.100\right)}{2.3.4+3.4.5+4.5.6+............+98.99.100}\)

\(a=3.2\)

\(a=6\)

Vậy a=6.

\(\frac{2.9.8+3.12.10+4.15.12+...+98.297.200}{2.3.4+3.4.5+4.5.6+...+98.99.100}=\frac{3.2.\left(2.3.4+3.4.5+4.5.6+...+98.99.100\right)}{2.3.4+3.4.5+4.5.6+...+98.99.100}=6\)

Ta có:

\(2.9.8+3.12.10+...+98.297.200\)

\(=2.3.4.3.2+3.4.5.3.2+...+98.99.100.3.2\)

\(=6.\left(2.3.4+3.4.5+...+98.99.100\right)\)

Thế lại bài toán (sửa đề luôn)

\(a=\frac{2.9.8+3.12.10+...+98.297.200}{2.3.4+3.4.5+...+98.99.100}\)

\(=\frac{6.\left(2.3.4+3.4.5+...+98.99.100\right)}{2.3.4+3.4.5+...+98.99.100}=6\)

\(\Rightarrow a^2=6^2=36\)

cái mẫu là 2 . 3 hay là 23 vậy ?

Mình thấy ý kiến của bạn alibaba nguyễn đúng rồi

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SAI ĐỀ RỒI BẠN. SỬA 23=2.3

\(\frac{2.9.8+3.12.10+4.15.12+...+98.297.200}{2.3.4+3.4.5+4.5.6+...+98.99.100}\)

\(\frac{1.2.3.\left(2.3.4+3.4.5+4.5.6+...+98.99.100\right)}{\left(2.3.4+3.4.5+4.5.6+...+98.99.10\right)}\)

\(=6\)

VẬYa²=6²=36

a có hoặc ko phải là nhiệm ...

Bài 3:

Ta có:

\(\frac{1}{2^2}\)+\(\frac{1}{3^2}\)+\(...\)+\(\frac{1}{2010^2}\)<\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+...+\(\frac{1}{2009.2010}\)

Xét:\(\frac{1}{1.2}\)+\(\frac{1}{2.3}\)+.....+\(\frac{1}{2009+2010}\)=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2009}-\frac{1}{2010}\)=\(1-\frac{1}{2010}\)<1

\(\Rightarrow\)\(\frac{1}{2^2}+\frac{1}{3^2}+....+\frac{1}{2010^2}< 1\)

\(\)Vậy \(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{2010^2}< 1\)

A=1(2+1)+2(3+1)+3(4+1)+...+99(100 +1 )

A=1.2+1+2.3+2+3.4+3...99.100+99

A=(1.2+2.3+3.4+...99.100)+(1+2+3+4...99)

giải:

Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100

4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100)4

4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)

4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100

4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101

4A=98.99.100.101

=>A=98.99.100.101/4

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