1) Assertion (A) if |x|<1, then ∑∞m=0(−1)nxn+1=xx+1 Reason (R) if |x|<1, then (1+x)−1 = 1−x+x2−x3+..... Which one of the following is true? A) (A) and (R) are true , (R) is correct explanation of (A) B) (A) and (R) are true but (R) is not a correct explanation of (A) C) (A) is true , but (R) is false D) (A) is false , but (R) is true Answer: Option AExplanation: We have, xx+1=x(1+x)−1=x(1−x+x2−x3+x4−...) = x−x2+x3−x4+x5− =∑∞n=0(−1)nxn+1 ∴ Assertion is true Reason (R)=(1+x)−1 = 1−x+x2−x3+..... is also true , (A) and (R) are true , (R) is correct explanation of (A)
