AmirElbanna

First Question

1/(1)(2) , 1/(2)(3) , 1/(3)(4)

The first three terms of a sequence are given. The nth term of the sequence is 1/(n)(n+1).

Which is equal to 1/(n)-(n-1). What is the sum of the first 50 terms of this sequence?


a) 1

b) 50/51

c) 49/50

d) 24/50

e) 1/(50)(51)


Second Question

Y=-2(x-2)^2 +3

In the xy-plane, line L passes through the point (4,-5) and the vertex of the parabola

with the equation above. What is the slope of line L ?

A) -4

b) -1/4

c) 0

d) 1/4

e) 4

Please I need the answers with persuasive explanation

rspence

1. The sum of the first 50 terms is

(1 - 1/2) + (1/2 - 1/3) + ... + (1/50 - 1/51)

Every term except 1 and -1/51 cancels (this is known as "telescoping"). The sum is 1 - 1/51 = 50/51.

2. Check out this thread:
Math Problems

AmirElbanna

I'm very thankful to you
But I have a question about the firsr solution» how have we come with 1. And -1\51

rspence

First term is 1 - 1/2 (or 1/1 - 1/2). The 50th term is 1/50 - 1/51. When you telescope, all of the intermediate terms (1/2, 1/3, ..., 1/50) cancel out, leaving 1 - 1/51.