32+22=...?
[ 22^32(32^23-23^22) - 32^23(22^32-23^22) ] : 23^22(32^23-22^32)
tính nhanh [22^32.(32^23-23^22)-32^28.(22^32-23^22)]:23^22.(32^23-22^32)
Nguyễn Quang Thành trả lời cụ thể đi
Tính nhanh:
C=23^22.(32^23-22^32)/22^32.(32^23-23^22)-32^23.(22^32-23^22)
Ta có 12 + 22 + 32 + …102 = 385
Suy ra ( 12 +22 + 32 +…+102 ) .32 = 385.32
Do đó ta tính được A = 32 + 62 + 92 + …+302 = 3465
Ta có 12 + 22 + 32 + …102 = 385
Suy ra ( 12 +22 + 32 +…+102 ) .32 = 385.32
Do đó ta tính được A = 32 + 62 + 92 + …+302 = 3465
Tính nhẩm:
12+9+19+2= 28+12+22+18=
79+1+71+9= 32+22+32+22=
12+9+19+2=32
28+12+22+18=80
79+1+71+9=160
32+22+32+22=108
12=9+19+2=42
28+12+22+18=80
79+1+71+9=160
32+22+32+22=108
Chúc bn hok giỏi
Chứng minh rằng:
A = 1/3 + 1/32 + 1/33 + ..........+ 1/399 < 1/2
B = 3/12x 22 + 5/22 x 32 + 7/32 x 42 +............+ 19/92 x 102 < 1
C = 1/3 + 2/32 + 3/33 + 4/34 +.........+ 100/3100 ≤ 0
\(A=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{99}}\)
\(\Rightarrow\dfrac{A}{3}=\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\)
\(\Rightarrow A-\dfrac{A}{3}=\dfrac{2A}{3}=\left(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}\right)-\left(\dfrac{1}{3^2}+\dfrac{1}{3^3}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{100}}\right)\)
\(\Rightarrow\dfrac{2A}{3}=\left(\dfrac{1}{3^2}-\dfrac{1}{3^2}\right)+\left(\dfrac{1}{3^3}-\dfrac{1}{3^3}\right)+...+\left(\dfrac{1}{3^{99}}-\dfrac{1}{3^{99}}\right)+\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)=\dfrac{1}{3}-\dfrac{1}{3^{100}}\)
\(\Rightarrow2A=3\cdot\left(\dfrac{1}{3}-\dfrac{1}{3^{100}}\right)\)
\(\Rightarrow\text{A}=\dfrac{1-\dfrac{1}{3^{99}}}{2}\)
\(\Rightarrow A=\dfrac{1}{2}-\dfrac{1}{2.3^{99}}< \dfrac{1}{2}\)
5, 72 + 7, 22 + 8, 72 + 10, 22 +...+ 32, 72 + 34, 22
khoảng cách là:
7,22-5,72=1,5
có số số hạng là:
(34,22-5,72):1,5+1=20(số)
tổng là:
(34,22+5,72)x20:2=399,4
đáp số 399,4 nha bạn
5, 72 + 7, 22 + 8, 72 + 10, 22 + ...+ 32, 72 + 34, 22 = ?
A=25.52-32-10
B=33.32+22+32
\(A=2^5.5^2-3^2-10\\ \\ A=32.25-9-10=800-9-10\\ \\ A=781\)
\(B=3^3.3^2+2^2+3^2\\ \\ B=3^{3+2}+4+9\\ \\ B=3^5+13=243+13\\ \\ B=256\)
Rút gọn các biểu thức sau: 2 2 - 3 2 + 2 . - 3 2 - - 1 4