giúp mik với mấy bạn giỏi toán ơi
Tính giá trị của biểu thức: A=202($200^{-2}$-1)($199^{-2}$-1)($198^{-2}$-1)…($101^{-2}$-1)
giúp mik với mấy bạn giỏi toán ơi
Tính giá trị của biểu thức: A=202($200^{-2}$-1)($199^{-2}$-1)($198^{-2}$-1)…($101^{-2}$-1)
Đáp án: $ A=\dfrac{201}{10100}$
Giải thích các bước giải:
Ta có:
$A=202(200^{-2}-1)(199^{-2}-1)(198^{-2}-1)…(101^{-2}-1)$
$\to A=202(\dfrac{1}{200^2}-1)(\dfrac{1}{199^2}-1)…(\dfrac{1}{101^2}-1)$
$\to A=202(1-\dfrac{1}{200^2})(1-\dfrac{1}{199^2})…(1-\dfrac{1}{101^2})$
$\to A=202\cdot \dfrac{200^2-1}{200^2}\cdot \dfrac{199^2-1}{199^2}….\dfrac{101^2-1}{101^2}$
$\to A=202\cdot \dfrac{(200-1)(200+1)}{200\cdot 200}\cdot \dfrac{(199-1)(199+1)}{199\cdot 199}….\dfrac{(101-1)(101+1)}{101\cdot 101}$
$\to A=202\cdot \dfrac{199\cdot 201}{200\cdot 200}\cdot \dfrac{198\cdot200}{199\cdot 199}….\dfrac{100\cdot102}{101\cdot 101}$
$\to A=\dfrac{199\cdot 198\cdot …\cdot 100}{200\cdot 199…101}\cdot \dfrac{202\cdot 201\cdot …102}{200\cdot 199\cdot …\cdot 101}$
$\to A=\dfrac{1}{200\cdot 101}\cdot 2\cdot 201$
$\to A=\dfrac{1}{100\cdot 101}\cdot 201$
$\to A=\dfrac{201}{10100}$
Đáp án:
Giải thích các bước giải:
Đáp án: A = 201 10100 A=20110100 Giải thích các bước giải: Ta có: A = 202 ( 200 − 2 − 1 ) ( 199 − 2 − 1 ) ( 198 − 2 − 1 ) . . . ( 101 − 2 − 1 ) A=202(200−2−1)(199−2−1)(198−2−1)…(101−2−1) → A = 202 ( 1 200 2 − 1 ) ( 1 199 2 − 1 ) . . . ( 1 101 2 − 1 ) →A=202(12002−1)(11992−1)…(11012−1) → A = 202 ( 1 − 1 200 2 ) ( 1 − 1 199 2 ) . . . ( 1 − 1 101 2 ) →A=202(1−12002)(1−11992)…(1−11012) → A = 202 ⋅ 200 2 − 1 200 2 ⋅ 199 2 − 1 199 2 . . . . 101 2 − 1 101 2
→A=202⋅2002−12002⋅1992−11992….1012−11012
→ A = 202 ⋅ ( 200 − 1 ) ( 200 + 1 ) 200 ⋅ 200 ⋅ ( 199 − 1 ) ( 199 + 1 ) 199 ⋅ 199 . . . . ( 101 − 1 ) ( 101 + 1 ) 101 ⋅ 101 →A=202⋅(200−1)(200+1)200⋅200⋅(199−1)(199+1)199⋅199….(101−1)(101+1)101⋅101
→ A = 202 ⋅ 199 ⋅ 201 200 ⋅ 200 ⋅ 198 ⋅ 200 199 ⋅ 199 . . . . 100 ⋅ 102 101 ⋅ 101 →A=202⋅199⋅201200⋅200⋅198⋅200199⋅199….100⋅102101⋅101
→ A = 199 ⋅ 198 ⋅ . . . ⋅ 100 200 ⋅ 199…101 ⋅ 202 ⋅ 201 ⋅ . . .102 200 ⋅ 199 ⋅ . . . ⋅ 101 →A=199⋅198⋅…⋅100200⋅199…101⋅202⋅201⋅…102200⋅199⋅…⋅101
→ A = 1 200 ⋅ 101 ⋅ 2 ⋅ 201
→A=1200⋅101⋅2⋅201 → A = 1 100 ⋅ 101 ⋅ 201
→A=1100⋅101⋅201 → A = 201 10100