Math help???

Question

Is there an easy way to calculate the following problem:

(1+1/2)(1+1/3)(1+1/4)............(1+1/102)(1+1/103)

Answer 1

Let's look at it like this...

(1/2 + 1/2 +1/2) (1+1/3) (1+1/4)............

The first term, is just 1 1/2

Now apply the third term (1 + 1/3) to the above.

What's (1 + 1/3) x (1/2 + 1/2 +1/2)? For the 1, we take 1/2 + 1/2 + 1/2, and for the 1/3, we take one of the 1/2's, so we get 1/2 + 1/2 +1/2 + 1/2.

The next term will add another 1/2, and so will the next...and the next, and so forth.

Each addional term...adds on 1/2. Therefore..

1 (1+1/2)(1+1/3)(1+1/4)............= 1 + 1/2 + 1/2 +1/2 .....

Which is infinite.

Answer 2

1+1/2 = 3/2
1+ 1/3 = 4/3
1+ 1/4 = 5/4
1+ 1/n = (n+1)/n

Answer 3

(1+1/2)=3/2
(1+1/3)=4/3
(1+1/4)=5/4
. . .
(1+1/n)=(n+1)/n
. . .
=> (3/2)*(4/3)*(5/4)*...*((n+1)/n)*...=1/2

Answer 4

(1 + 1/2) can be rewritten as 3/2
(1 + 1/3) is 4/3
(1 + 1/4) is 5/4
etc

So, now you have:

(3/2)(4/3)(5/4)...[(n+1)/n]

Written that way, you can see that most of the numerators and denominators cancel out...

You'll be left with (1/2)(n+1)

Answer 5

1+1/2 = 3/2
1+ 1/3 = 4/3
1+ 1/4 = 5/4
.
.
.
1+ 1/n = (n+1)/n

3/2 * 4/3 * 5/4 * ...* (n+1)/n = (n+1)/2

Answer 6

Get the common denominator of all the numbers even though there is no equation which is 12 and convert them to

(12 + 3) (6 + 3)(6+4)
(14)(9)(10)

1260 / 12

105 Which is complete wrong!!!!

Answer 7

Yes, by using excel

In column A input 2,3,4,5....n starting with cell A1 until cell An where n is until what number you need to compute

In cell B1 type the formula "=1+(1/A1)"; click cell B1 then drag down until Bn

In cell C2 type the formula "=B1*B2"

In cell C3 type the formula "=B3*C2"; click cell C3 then drag down until Cn

Cell Cn contains your answer...the others just gave the formula without showing how to calculate.