Evaluate
With step by step explanation !​

It's easier to deal with the symbolic sum (in sigma notation),

Expanding the terms in the fraction, computing the quotient, and decomposing into partial fractions gives

and it's the latter two terms that reveal a telescoping pattern.

In case you need more details about the partial fraction decomposition, we are looking for coefficients a and b such that

or

which gives a = 1, and a + b = 0 so that b = -1.

Our sum has been rearranged as

The remaining telescoping sum is

1/2 [(1/1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + … + (1/48 - 1/49) + (1/49 - 1/50) + (1/50 - 1/51)]

and you can see how there are pairs of numbers that cancel, so that the sum reduces to

1/2 [1/1 - 1/51] = 1/2 [1 - 1/51] = 1/2 × 50/51 = 25/51

So, our original sum ends up being

connie < felicia < stew

step-by-step explanation:

stew:

we need to find the slope

m = (y2-y1)/ (x2-x1)

    = (2650-795)/(10-3)

    = 1855/7

265 words per minute

connie:

we need to find the slope

m = (y2-y1)/ (x2-x1)

we have two points (0,0) and (4,800)

m = (800-0)/(4-0)

  m = 800/4

    200 words per minute

felicia:

260 words per minute

200< 260 < 265

connie < felicia < stew

answer: get jesus in your life

step-by-step explanation: