Question

chứng minh biểu thức sau ko phải số tự nhiên 

1/4+1/16+1/36+1/64+1/100+1/44+1/196+1/256

giúp mình nhanh nha

 

Answer 1

1/4+1/16=1\20

1\20+1/36=1/56

1/56+1/64=1\120

1/120+1/100=1/220

1/220+1/44=1/264

1/264+1/196=1/460

1/460+1/256=1/716

suy ra:1/716 ko phải số TN

Answer 2

Ta có : \(A=\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+...+\frac{1}{256}>0\)

\(A=\frac{1}{4}+\frac{1}{16}+\frac{1}{36}+\frac{1}{64}+\frac{1}{100}+\frac{1}{144}+\frac{1}{196}+\frac{1}{256}\)

\(A< \frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\frac{1}{36}+\frac{1}{49}+\frac{1}{64}\)\(+\frac{1}{81}+\frac{1}{100}+\frac{1}{121}+\frac{1}{144}+\frac{1}{169}+\frac{1}{196}+\frac{1}{225}+\frac{1}{256}\)

\(A< \frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{15\cdot16}\)

\(A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{15}-\frac{1}{16}\)

\(A< 1-\frac{1}{16}< 1\)

\(\Rightarrow0< A< 1\)

=> A ko là số tự nhiên