5. (-1)301 + (-1)302 + (-1)303 + ... + (-1)400
(a) 1
(b) 101
(c) 100
(d) 0
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Wrong Answer
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Answer:0
We know ( − 1 ) x (-1)x = − 1 =-1, when x is odd. = 1 =1 , when x is even. ∴ ( − 1 ) 301 + ( − 1 ) 302 + ... . + ( − 1 ) 400 ∴(-1)301+(-1)302+....+(-1)400 = ( − 1 ) + 1 + ( − 1 ) + 1 + ... ( 100 terms ) = 0 =(-1)+1+(-1)+1+...(100 terms)=0 Hence, the correct options is (d)
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