Find 1/ ( 3 × 7 ) + 1/ ( 7 × 11 ) + 1/ ( 11 × 15 ) + ⋯ to infinity.

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Find $1/ (3 \times 7) + 1/ (7 \times 11) + 1/ (11 \times 15) + \dots$ to infinity.

Answer:

Solution:

Use $1/ [x (x + 4)] = (1/ x - 1/ (x + 4)) /4$ . The series telescopes to $(1/4) (1/3) = 1/12$ .

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

⏱ 2mℹ️ Source: QB

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