Need an answer showing work thax!

Option (a)

Step-by-step explanation:

The given expression is :

We need to rewrite the sum using sigma notation.

The numerator is 3 in all terms.

At denominator, in first term (1)(2), in second term (2)(3) and so on.

A general term for the denominator is k(k+1).

Sigma notation is :

Hence, the correct option is (A).

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.