# Simplifying the Expression

## Homework Statement

[/B]
Simplify:

$$\frac{5\cdot 8\cdot 11 \cdots (3i+2)}{2\cdot 5 \cdot 8 \cdots (3i-1)}$$

## The Attempt at a Solution

I realize the numerator and denominator terms cancel besides the 2, however I'm struggling to write this in a proper form. Only just started sequences, haven't introduced infinite products or sigmas, or anything along those lines. Some insight would be appreciated.

Student100
Gold Member

## Homework Statement

[/B]
Simplify:

$$\frac{5\cdot 8\cdot 11 \cdots (3i+2)}{2\cdot 5 \cdot 8 \cdots (3i-1)}$$

## The Attempt at a Solution

I realize the numerator and denominator terms cancel besides the 2, however I'm struggling to write this in a proper form. Only just started sequences, haven't introduced infinite products or sigmas, or anything along those lines. Some insight would be appreciated.

Just the two?

Euler2718
vela
Staff Emeritus
Homework Helper
What do you mean by "proper form"?

Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

[/B]
Simplify:

$$\frac{5\cdot 8\cdot 11 \cdots (3i+2)}{2\cdot 5 \cdot 8 \cdots (3i-1)}$$

## The Attempt at a Solution

I realize the numerator and denominator terms cancel besides the 2, however I'm struggling to write this in a proper form. Only just started sequences, haven't introduced infinite products or sigmas, or anything along those lines. Some insight would be appreciated.

You say you realize that the numerator and denominator terms cancel, but I don't understand what is preventing you from just going ahead and cancelling them.

Euler2718
Just the two?

I was thinking,

$$\frac{3i+2}{2}$$

Because the previous term of the numerator should cancel with the 3i-1 as the pattern suggests.

Student100
Gold Member
I was thinking,

$$\frac{3i+2}{2}$$

Because the previous term of the numerator should cancel with the 3i-1 as the pattern suggests.

Okay, that's what you meant, not ##\frac{1}{2}##. That's it.

Euler2718
Okay, that's what you meant, not ##\frac{1}{2}##. That's it.

Thanks. Been a bit sick lately; really appreciate the help on this forum.

Student100
Gold Member
Thanks. Been a bit sick lately; really appreciate the help on this forum.

If you need to prove it to yourself take the first 5 terms of the sequence, and simplify. Then take i = 5 and put it into the expression you just wrote. It'll be the same. What kind of insights were you looking for?

Euler2718
If you need to prove it to yourself take the first 5 terms of the sequence, and simplify. Then take i = 5 and put it into the expression you just wrote. It'll be the same. What kind of insights were you looking for?

Maybe insights wasn't the proper word. I was at it a while getting no-where so I was hoping for a kick in the right direction, as was the case.

HallsofIvy