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Ex 9.1, 12 - Write five terms series a1 = -1, an = an-1/n - Finding sum from series

  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
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Ex9.1 , 12 Write the first five terms of the following sequence and obtain the corresponding series:Β  a1 = -1 , an = π‘Ž_(π‘›βˆ’1)/𝑛 , n β‰₯ 2 It is given that a1 = -1, For a2 and onward, we have to use this formula an = π‘Ž_(π‘›βˆ’1)/𝑛 Putting n = 2 in (1) a2 = π‘Ž_(2βˆ’1)/2 = π‘Ž_1/2 = (βˆ’1)/2 Putting n = 3 in (1) a3 = π‘Ž_(3 βˆ’ 1 )/3 a3 = (a2βˆ’)/3 a3 = ((βˆ’1)/2)/3 a3 = ((βˆ’1)/2)(1/3) a3 = (βˆ’1)/6 Putting n = 4 in (1) a4 = π‘Ž_(4 βˆ’ 1 )/4 a4 = a3/4 a4 = ((βˆ’1)/6)/4 a4 = ( (βˆ’1)/6 )(1/4) a4 = (βˆ’1)/24 Putting n = 5 in (1) a5 = π‘Ž_(5 βˆ’ 1 )/5 a5 = (a4βˆ’)/5 a5 = ((βˆ’1)/24)/5 a5 = ((βˆ’1)/24)(1/5) a5 = (βˆ’1)/120 Hence first five terms of the sequence are -1, (βˆ’1)/2, (βˆ’1)/6, (βˆ’1)/24, and (βˆ’1)/120. The corresponding series is (-1) + ((βˆ’1)/2) + ((βˆ’1)/6) + ((βˆ’1)/24) + ((βˆ’1)/120) +……

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