True or false

Algebra Level 3

1 n 2 − 1 ( n + 1 ) 2 = ( 1 n − 1 n + 1 ) ( 1 n + 1 n + 1 ) \dfrac{1}{n^2}-\dfrac{1}{(n+1)^2}=\left(\dfrac{1}{n}-\dfrac{1}{n+1}\right)\left(\dfrac{1}{n}+\dfrac{1}{n+1}\right)

Is the equation above for all non-zero n n ?

False True

Aareyan Manzoor by Aareyan Manzoor , 18, USA

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1 solution

Aareyan Manzoor
Dec 12, 2015

at n=-1, both sides are undefined, and undefined ≠ undefined, so for one case, it isfalse. so the whole statement is false.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Hello erm... I don't understand why you have made it level 3 sum.... Because this is a very basic sum... Level 2 would have been right....

Debmalya Mitra - 5 years, 6 months ago

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moderator changed it, i set it level 1 originally.

Aareyan Manzoor - 5 years, 6 months ago

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Ha ha... Well I won't understand that... as I have never posted any sum in brilliant....

Debmalya Mitra - 5 years, 6 months ago

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