1/6 n (n+1) ( n+2) - 1/6 n-1 (n) (n+1) = 1/2 n (n+1)
I am solving this with the assumption that all the n terms are in the numerator and 6 is in the denominator. (That's the only way to arrive at the answer.)
The factors common in both sides can be taken out.
(1/6)n(n+1) can be taken out
1/6 n (n+1) ( n+2) - 1/6 n-1 (n) (n+1)
= 1/6 n (n+1) [(n+2)-(n-1)]
=1/6 n (n+1) [n + 2 - n + 1)]
=1/6 n (n+1) [n - n + 2 + 1]
=1/6 n (n+1) [2 + 1]
=1/6 n (n+1) [3]
= 3/6 n (n+1)
= 1/2 n (n+1)
long equation !! stuck
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Brent@GMATPrepNow
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This one of those equations where plugging the answer choices might be the fastest approach.marmar29 wrote:hello everyone
i really do stuck in this equaiton to make it simple one |& get the final results
1/6 n (n+1) ( n+2) - 1/6 n-1 (n) (n+1) = 1/2 n (n+1)
please show me the steps
thanks
For example, checking an answer choice like n=0 would take only seconds to verify. In turn, this would help eliminate your options, etc.
(1/6)(n)(n+1)( n+2) - (1/6)(n-1)(n)(n+1) = (1/2)(n)(n+1)
Also notice that, since each of the 3 products here features n, we can see that n=0 is one possible solution.
Likewise, since each of the 3 products here features n+1, we can see that (n+1)=0 is another possible solution (i.e., n = -1)
Cheers,
Brent
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Stuart@KaplanGMAT
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First up, what's the question? Solve for a possible value of n? Solve for all the values of n? Without the question (and choices), it's impossible to find the best possible approach.marmar29 wrote:hello everyone
i really do stuck in this equaiton to make it simple one |& get the final results
1/6 n (n+1) ( n+2) - 1/6 n-1 (n) (n+1) = 1/2 n (n+1)
please show me the steps
thanks
Assuming that we need all the values of n, I'd start with Brett's analysis:
n is common to all 3 terms, so n=0 works (you'd get 0 - 0 = 0, which is correct). Eliminate any choices that don't contain 0.
(n+1) is common to all 3 terms, so n=-1 works (you'd again get 0 - 0 = 0, which is correct). Eliminate any remaining choices that don't contain -1.
Assuming that there's more than 1 choice remaining, divide both sides by (n)(n+1) to get:
(1/6)(n+2) - (1/6)(n-1) = 1/2
(Note: we can only do this step because we're now assuming that n doesn't equal 0 or -1.)
Multiply both sides by 6:
(n+2) - (n-1) = 3
Simplify:
3 = 3
No more "n"s, so there are no other possible values.
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