Question

a = 1/2016 - 2/2016 + 3/2016 - 4/2016 + 5/2016 - ... - 2016/2016

determine the value of a!
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Answer 1

a = 1/2016 - 2/2016 + 3/2016 - 4/2016 + 5/2016 - ... - 2016/2016

= 1/2016 - 2/2016 = -1/2016

= 3/2016 - 4/2016 = -1/2016

......

= 2015/2016 - 2016/2016 = -1/2016

So 2016 term reduce to 1008. Numerator of every term is -1 & denominator of every term is 2016.

Now the value of a :

a = - 1/2016 + - 1/2016 + ..... + - 1/2016 [Total term = 1008]

Since denominator is same the value of a became,

a = -1008/2016 = -1/2

Answer 2

Step-by-step explanation:

a = 1/2016 - 2/2016 + 3/2016 - 4/2016 + 5/2016 - 2016/2016

a = 1/2016 - 2/2016 + 3/2016 - 4/2016 + 5/2016 - 2016/2016= 1/2016 - 2/2016 = -1/2016

a = 1/2016 - 2/2016 + 3/2016 - 4/2016 + 5/2016 - 2016/2016= 1/2016 - 2/2016 = -1/2016= 3/2016 - 4/2016 = -1/2016= 2015/2016 - 2016/2016 = -1/2016So 2016 term reduce to 1008. Numerator of every term is -1 & denominator of every term is2016.Now the value of a :a =. 1/2016 +- 1/2016 + - 1/2016 [Total term = 1008]

Since denominator is same the value of a became

= -1008/2016 = -1/2

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