​If A = (-1)1 + (-1)2 + (-1)3 + .... + (-1)1001 and B = (-1)1 - (-1)2 + (-1)3 - (-1)4 + .... + (-1)1001, then find A - B. 

Dear Student ,
 
Please find below the solution to the asked query :

A-B = -11+-12+-13+.....+-11000 - -11--12+-13--14.....+-11000Terms having odd powers get cancelled out on solving and terms having even powers get add up.=2 -12+ 2-14 + 2-16 + .......... + 2-11000=2  -12+ -14 + -16 + .......... + -11000 Even power of -1 = 1=2 1+1+1 .... + 1             There are total 500 terms=2 500=1000   ANS...
 
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-2
 
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- 1^odd no. = -1
+1^even no. = +1
there are 1001 ones ,500 postive,500 negative and 1 neg. 
in A-
500 pos +500 neg =0 plus one neg.= -1
in B 
THE SUBTRACTION OF ONE POS AND NEGATIVE INTEGER =ADDITION 
asin a same thing is in B and answer is -1 so A + B = -2
  • -1
-2
  • -1
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