(1+3-1)(1+3-2)(1+3-4)(1+3-8)…..(1+3-2n) is equal to
321+3-2n
321-3-2n
321-3-2n+1
noneofthese
Explanation for the correct option:
Let the given series be, S=(1+3−1)(1+3−2)(1+3−4)...(1+3−2n)
Multiplying both sides by (1−3−1),
⇒(1−3−1)S=(1−3−1)(1+3−1)(1+3−2)(1+3−4)...(1+3−2n)
⇒ 23S=(1−3−2)(1+3−2)(1+3−4)...(1+3−2n)
⇒ 23S=1−(3−2n)2
⇒ 23S=1−3−2n1+3−2n ∵a2-b2=(a-b)(a+b)
⇒ 23S=(1−3−2n+1)
⇒ S=32(1−3−2n+1)
Hence, Option ‘C’ is Correct.
Find the value of:
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