one If the sum of the first n items in the sequence is Sn, what is the sum of the first 2009 items? n(n+1)

1 / N (n + 1) = [(n + 1) - n] / N (n + 1) = 1 / n-1 / (n + 1), so Sn = 1-1 / 2 + 1 / 2-1 / 3 +... + 1 / n-1 / (n + 1) = 1-1 / (n + 1), so s2009 = 1-1 / 2010 = 2009 / 2010

Important knowledge points in mathematical derivative in Senior High School Let's summarize

I don't know which province or city you are taking the college entrance examination
Take Beijing as an example, half of the college entrance examination derivatives are placed in the penultimate question, with a score of about 13 points
If you want to get a better university, you must get a full score on the question of derivative
So the derivative problem won't be too difficult
Pay special attention to the derivation of LNX, a ^ x, loga X
First of all, in the derivative problem during the examination, the derivative is mostly in the form of fraction, the denominator is generally constant > 0, and the numerator is generally a quadratic function
Normally, this quadratic function is a function with quadratic term coefficients
Then we can start the classified discussion
Classification discussion point 1: discuss whether the coefficient of quadratic term is equal to 0
Of course, if the person making the question is very kind, maybe it just doesn't exist
Here you should also refer to the answer of the first question appropriately. The person who makes the question will guide your thinking
Classified discussion point 2: Discussion △
For example, if the opening is upward, △ 0, then factorization can be considered
Normally, no one will let you use the root formula. It's meaningless to test this
Pay attention to the comprehensive application of classification discussion points 2 and 3, and draw a picture, thread a needle (pay attention to the negative sign) or directly draw the original function image, so the probability of error will be lower
We should pay attention to the calculation of derivatives. For example, the roots are 1 / (a + 1) and 1 / (A-1). Many people will be wrong when discussing the two sizes of a on (0,1) and a on (1, + infinity)

Summary of mathematical derivative knowledge in Senior High School

1. Simple derivation formula
2. Find monotone interval
3. Find the extreme value of the function
4. Maximum value

A knowledge point of mathematical derivative in Senior High School By the way, what does continuity mean? Is segmentation continuous? Assuming f (x) = x (0 ≤ x < 1), f (x) = x + 1 (1 ≤ x ≤ 2), is f (x) a continuous function?

Continuity only requires that the function values of the left limit, the right limit and the point are equal. In the case of segmentation, it is OK as long as this point is satisfied. However, "derivability must be continuous, and continuity must not be derivable". The requirement of derivability is somewhat different from that of continuity. If the piecewise derivative function of the function exists, The value on the left and the value on the right of the derivative function of the function on the segment point should be consistent. Note: the function expression of the derivative function on both sides of the segment point is not necessarily the same. Just look at the basic definitions of continuity and derivation. Without a formula editor, you can only talk about it briefly

Ask high school math questions Find the derivative of y = X4 (the meaning of the fourth power) - x2-x-3 and help write the detailed process

solution
y=x^4-x^2-x-3
y'=(x^4)'-(x^2)'-(x)'-(3)'
y‘=4x ³- 2x-1

Elective of mathematics people's Education Edition, problems in conic curve and equation 1. The parabola y = - X2 (square) / 2 intersects the straight line L passing through M (0, - 1) at two points a and B, and O is the origin. If the sum of the slopes of OA and ob is 1, find the equation of straight line L 2. The center is at the origin, the abscissa of the midpoint of an ellipse with focus f (0, 50 under the root sign) cut by the straight line L: y = 3x-2 is 1 / 2, and the elliptic equation is solved 3. Ellipse x ²/ 45+y ²/ The focal points of 20 = 1 are F1 and F2 respectively. The straight line passing through the origin O and the ellipse intersect at two points a and B. if the area of triangle Abf1 is 20, find the straight line AB equation 4. Ellipse x ²/ 12+y ²/ The focal points of 3 = 1 are F1 and F2 respectively, and the point P is on the ellipse. If the midpoint of Pf1 is on the y-axis, how many times is Pf1 ｜ PF2 ｜?

1. The parabola y = - X2 (square) / 2 intersects the straight line L passing through M (0, - 1) at two points a and B, and O is the origin. If the sum of the slopes of OA and ob is 1, find the equation of straight line L
Let y = kx-1, y = - X2 (square) / 2, a (x1, Y1), B (X2, Y2), KOA = Y1 / x1, kob = Y2 / x2
Y1 = - X12 (square) / 2, y21 = - X22 (square) / 2,
y1/x1=-x1/2,y2/x2=-x2+2,-(x1+x2)/2=1
Simultaneous y = kx-1, y = - X2 (square) / 2
Get x ^ 2 + 2kx-2 = 0 X1 + x2 = - 2K k = 1, linear equation y = X-1
2. The center is at the origin, the abscissa of the midpoint of an ellipse with focus f (0, 50 under the root sign) cut by the straight line L: y = 3x-2 is 1 / 2, and the elliptic equation is solved
Elliptic equation MX ^ 2 + NY ^ 2 = 1,
The abscissa of the midpoint cut by y = 3x-2 is 1 / 2, the ordinate is - 1 / 2, and the straight line and ellipse intersect at a (x1, Y1),
B (X2, Y2) is substituted into the ellipse and subtracted to obtain m (x1-x2) (x1 + x2) + (y1-y2) (Y1 + Y2) = 0,
Straight line k = 3 = y1-y2 / x1-x2, X1 + x2 = 1, Y1 + y2 = - 1
m-3n=0,1/n-1/m=50,n=1/75,m=1/25
x^2/25+y^2/75
3. Ellipse x ²/ 45+y ²/ The focal points of 20 = 1 are F1 and F2 respectively. The straight line passing through the origin O and the ellipse intersect at two points a and B. if the area of triangle Abf1 is 20, find the straight line AB equation
Y = KX, a, B are symmetric about the origin
S triangle Abf1 = s triangle AOF1 + s triangle bof1 = 1 / 2C (y1-y2) = cy1 (let Y1 > Y2)
C = 5, Y1 = 4, substituted into ellipse, x = 3, x = - 3
Y = 4x / 3 or y = - 4x / 3
4. Ellipse x ²/ 12+y ²/ The focal points of 3 = 1 are F1 and F2 respectively, and the point P is on the ellipse. If the midpoint of Pf1 is on the y-axis, how many times is Pf1 ｜ PF2 ｜?
｜ Pf1 ｜ + ｜ PF2 ｜ = 2A = 4 radical 3, the midpoint m is on the y-axis, Mo / / F2P, F2P is perpendicular to the x-axis
｜ Pf1 ｜ ^ 2 - ｜ PF2 ｜ ^ 2 = 4C ^ 2 = 36, ｜ Pf1 ｜ + ｜ PF2 ｜ = 4 root 3
｜ Pf1 ｜ - ｜ PF2 ｜ = 3 root number 3, ｜ Pf1 ｜ = 7 root number 3 / 2, ｜ PF2 ｜ = root number 3 / 2
｜ Pf1 ｜ is 7 times that of ｜ PF2 ｜

one If the sum of the first n items in the sequence is Sn, what is the sum of the first 2009 items? n(n+1)