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Q.

If ∑r=1n Tr=3n−1, then find the sum of ∑m=1n 1Tm.

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a

3413n

b

341−13n

c

341−12n

d

341−15n

answer is B.

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Detailed Solution

∑r=1nTr=3n−1⇒Tr=3r-1-3r−1−1=3r−1(3−1)=23r−1⇒1Tr=12×13r−1⇒∑r=1n 1Tr=12∑r=1n 13r−1=121−13n1−13=341−13n

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If ∑r=1n Tr=3n−1, then find the sum of ∑m=1n 1Tm.