Define T r = ( 1 + 2 + ⋯ + r ) 2 / ( 1 + 3 + ⋯ + ( 2 r − 1 )) , and S = T 1 + T 2 + ⋯ . Which statements are true?

The denominator is r 2 and T r = ( r + 1 ) 2 /4 . Thus T 7 = 16 and ∑ r = 1 10 ( r + 1 ) 2 /4 = ( 385 + 110 + 10 ) /4 = 505/4 .

Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesSpecial sequences/seriesMedium2 minQB

MathematicsMediummultiple choice

Define $T_{r} = (1 + 2 + \dots + r)^{2} / (1 + 3 + \dots + (2 r - 1))$ , and $S = T_{1} + T_{2} + \dots$ . Which statements are true?

Answer:

A, C

Solution:

The denominator is $r^{2}$ and $T_{r} = (r + 1)^{2} /4$ . Thus $T_{7} = 16$ and $\sum_{r = 1}^{10} (r + 1)^{2} /4 = (385 + 110 + 10) /4 = 505/4$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Special sequences/series

⏱ 2mℹ️ Source: QB

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