Question

If x=(-1)' + (-1)2 + ...... + (-1)2009 and y=(-1)' -
(-1) + (-1)-(-1)* + ... + (-1)2009, then find x - y.
(A) 2009 (B) 2008 (C)0 (D) 1004​

Answer 1

Given : x = (-1)¹  + (-1)²  + (-1)³  + . + . + . + . + (-1)²⁰⁰⁹

y = (-1)¹  -  (-1)²  + (-1)³  + . - . + . - . + (-1)²⁰⁰⁹

To Find :  x - y

(A) 2009 (B) 2008 (C)0 (D) 1004​

Solution:

x = (-1)¹  + (-1)²  + (-1)³  + . + . + . + . + (-1)²⁰⁰⁹

=> x = - 1 + 1 - 1 + 1 + . + . + . + .   - 1

=> x =   - 1

y = (-1)¹  -  (-1)²  + (-1)³  + . - . + . - . + (-1)²⁰⁰⁹

=> y = - 1 - 1 - 1 - 1 - . -  -  .  -    - 1

=> y = - 2009

x - y

= - 1 - (-2009)

= - 1 + 2009

= 2008

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find x - y.

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