biểu thứ là gì?

M = 5 + 5² + 5³ + ... + 5²⁰¹².

    = ( 5+1 ).5² + ( 5+1 ). 5³ +...+( 5+1 ). 5 ⁸⁰

    =6. 5² + 6. 5³ + ...+ 6. 5 ⁸⁰

    =\(6\).5².5³x...x5 ⁸⁰

Vậy M chia hết cho 6.

Sửa N=\(\frac{2}{3}.\frac{4}{5}.\frac{6}{7}.....\frac{100}{101}\)

Ta có : \(\frac{1}{2}< \frac{2}{3}\); \(\frac{3}{4}< \frac{4}{5}\); \(\frac{5}{6}< \frac{6}{7}\); ... ; \(\frac{99}{100}< \frac{100}{101}\)

\(\Rightarrow\)\(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}< \frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}\)hay M < N

b) M .N = \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}.\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}=\frac{1.2.3.4.5.6...99.100}{2.3.4.5.6.7...100.101}=\frac{1}{101}\)

c) vì M < N nên M. M < M . N = \(\frac{1}{101}\)\(< \frac{1}{100}\)

\(\Rightarrow M< \frac{1}{10}\)

bài 1 mifk viết sai nha.

bài 1: cho A=1+3+3\(^2\)+3\(^3\)+...+3\(^{10}\).Tìm số tự nhiên n biết 2 x A + 1 = 3\(^n\)

B1:

\(A=1+3+3^2+3^3+...+3^{10}\\ 3A=3+3^2+3^3+3^4+...+3^{11}\\ 3A-A=3^{11}-1\\ \Rightarrow A=\frac{3^{11}-1}{2}\)

mấy câu khác tương tự nha

Bài 2:

M = 1/2.3/4.5/6...99/100

Ta có: \(\frac{a}{b}\) = 1 - \(\frac{b-a}{b}\) (a; b; n ∈ N* và b > a)

\(\frac{a+n}{b+n}\) = 1 - \(\frac{b-a}{b+n}\)

\(\frac{a}{b}\) < \(\frac{a+n}{b+n}\)

Áp dụng công thức trên ta có:

\(\frac12<\frac{1+1}{2+1}=\frac23\)

\(\frac34<\frac{3+1}{4+1}=\frac45\)

\(\frac56\) < \(\frac{5+1}{6+1}\) = \(\frac67\)

............................

\(\frac{99}{100}\) < \(\frac{99+1}{100+1}\) = \(\frac{100}{101}\)

Cộng vế với vế ta có:

M = \(\frac12\).\(\frac34\).\(\frac56\)...\(\frac{99}{100}\) < \(\frac23\).\(\frac45\)..\(\frac{100}{101}\) = N

M < N (đpcm)

b; M.N = \(\frac12\).\(\frac34\).\(\frac56\)...\(\frac{99}{100}\).\(\frac23\).\(\frac45\)..\(\frac{100}{101}\)

M.N = \(\frac{1.3.5\ldots99}{3.5\ldots101}\). \(\frac{2.4.6\ldots100}{2.4.6\ldots100}\)

M.N = 1/100.101

các bạn ơi giúp mìh với mìh đag cần gấp ai nhanh và đúng thì mih tick cho

tick mình đi mình giải cho

\(-5\left(x+\dfrac{1}{5}\right)-\dfrac{1}{2}\left(x-\dfrac{2}{3}\right)=\dfrac{3}{2}x-\dfrac{5}{6}\\ -5x+-5.\dfrac{1}{5}-\dfrac{1}{2}x-\dfrac{1}{2}.\dfrac{2}{3}=\dfrac{3}{2}x-\dfrac{5}{6}\\ -5x+\dfrac{-5}{5}-\dfrac{1}{2}x-\dfrac{2}{6}=\dfrac{3}{2}x-\dfrac{5}{6}\)

\(-5x+\left(-1\right)-\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{3}{2}x-\dfrac{5}{6}\\ -5x-1-\dfrac{1}{2}x-\dfrac{1}{3}=\dfrac{3}{2}x-\dfrac{5}{6}\\ x.\left(-5-\dfrac{1}{2}\right)-1-\dfrac{1}{3}=\dfrac{3}{2}x-\dfrac{5}{6}\\ x.\dfrac{-11}{2}-1-\dfrac{1}{3}=\dfrac{3}{2}x-\dfrac{5}{6}\\ x.\dfrac{-11}{2}-1=\dfrac{3}{2}x-\dfrac{5}{6}+\dfrac{1}{3}\\ x.\dfrac{-11}{2}-1=\dfrac{3}{2}x-\left(\dfrac{5}{6}-\dfrac{1}{3}\right)\\ x.\dfrac{-11}{2}-1=\dfrac{3}{2}x-\dfrac{1}{2}\\ x.\dfrac{-11}{2}=\dfrac{3}{2}x-\left(\dfrac{1}{2}-1\right)\\ x.\dfrac{-11}{2}=\dfrac{3}{2}x-\dfrac{-1}{2}\)

Mình bí rùi! Có chỗ nào sai bạn nhắc mk nhé

Ta có: + + + ≤ x <

⇒10-12+5-6/30≤ x< -105+40-35+84+100/140

⇒-3/30≤ x <84/140

⇒-0,1≤ x < 0,6

⇒x=0

\(4\frac{2}{5}+5\frac{6}{9}+2\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)

\(=4+\frac{2}{5}+5+\frac{6}{9}+2+\frac{3}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)

\(=\left(4+5+2\right)+\left(\frac{2}{5}+\frac{3}{5}\right)+\left(\frac{6}{9}+\frac{1}{3}\right)+\left(\frac{3}{4}+\frac{1}{4}\right)\)

\(=11+1+1+1\)

\(=14\)

\(=\frac{22}{5}+\frac{17}{3}+\frac{11}{4}+\frac{3}{5}+\frac{1}{3}+\frac{1}{4}\)

\(=\left(\frac{22}{5}+\frac{3}{5}\right)+\left(\frac{11}{4}+\frac{1}{4}\right)+\left(\frac{17}{3}+\frac{1}{3}\right)\)

\(=5+3+6=14\)

a) Ta có :

M= \(5+5^2+5^3+...+5^{60}\)

5M= \(5^2+5^3+5^4+...+5^{61}\)

5M - M= \(\left(5^2+5^3+5^4+...+5^{61}\right)\) - \(\left(5+5^2+5^3+...+5^{60}\right)\)

4M= \(5^{61}-5\)

M= \(\dfrac{5^{61}-5}{4}\)