If the intersection of the image of the linear function y = - K / K + 1 x + 1 / K + 1 (k is a natural number) and the x-axis and y-axis is a, B.O. let the area of RT △ ABO be SK, then (1) find S1 (2) find S1 + S2 + S3 + +Value of s2010

If the intersection of the image of the linear function y = - K / K + 1 x + 1 / K + 1 (k is a natural number) and the x-axis and y-axis is a, B.O. let the area of RT △ ABO be SK, then (1) find S1 (2) find S1 + S2 + S3 + +Value of s2010

At the beginning, I was really puzzled by this topic It took a while to understand
According to the function of the topic, we can find that this function intersects with X axis at (1 / K, 0) and Y axis at (0,1 / (K + 1));
Because SK = 1 / k * (1 / (K + 1)) / 2
So, the original formula is 1 / 2 * ((1 / (1 * 2)) + 1 / (2 * 3) + 1 / (3 * 4) + +1/（2010*2011）)
=1/2*(1/1-1/2+1/2-1/3+1/3-1/4+… +1/2010-1/2011)
=1/2*(2010/2011)
=1005/2011
This problem mainly involves the formula 1 / N (n + 1) = 1 / N - 1 / (n + 1)
How to prove this formula Well It's OK to divide it all~

Is y = 2 (x-1) a positive proportional function?
Do you have any skills to judge this kind of questions? Do you have any influence on the score, root sign and negative number?
Is y = - 8x negative an inverse proportional function?

No constant term is a positive proportion

Given the positive scale function y = (2m + 4) x, find:
① When m is the value, the function image passes through one or three quadrants
② When m is the value of M, y decreases with the increase of X
③ When m is the value, the point (1,3) is on the function image

Given the positive proportion function y = (2m + 4) X
(1) When m is the value, the function image passes through one or three quadrants;
(2) When m is the value, y decreases with the increase of X;
(3) When m is the value, the point (1,3) is on the function image;
(2) According to the fact that y decreases with the increase of X, the inequality of M is listed, and the range of M can be obtained;
(3) The point (1,3) is directly substituted into the positive scale function y = (2m + 4) x, and the value of M can be obtained. (1) the image of function passes through one or three images,
2 m + 4 ＞ 0, m ＞ - 2;
(2) ∵ y decreases with the increase of X,
2 m + 4 ＜ 0, m ＜ - 2;
(3) ∵ point (1,3) is on the graph of the function,
The key to solve this problem is that when k ＞ 0, the function image passes through one or three quadrants; when k ＜ 0, the function image passes through two or four quadrants, and Y decreases with the increase of X

The positive scale function y = KX is a straight line passing through the origin. The image of drawing it often selects two points (), () to make a straight line?

(0,0) and (1, K)