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: a1 = -1 , an = ๐‘Ž_(๐‘›โˆ’1)/๐‘› , n โ‰ฅ 2 It is given that a1 = -1, For a2 and onward, we have to use this formula an = ๐‘Ž_(๐‘›โˆ’1)/๐‘› Putting n = 2 in (1) a2 = ๐‘Ž_(2โˆ’1)/2 = ๐‘Ž_1/2 = (โˆ’1)/2 Putting n = 3 in (1) a3 = ๐‘Ž_(3 โˆ’ 1 )/3 a3 = (a2โˆ’)/3 a3 = ((โˆ’1)/2)/3 a3 = ((โˆ’1)/2)(1/3) a3 = (โˆ’1)/6 Putting n = 4 in (1) a4 = ๐‘Ž_(4 โˆ’ 1 )/4 a4 = a3/4 a4 = ((โˆ’1)/6)/4 a4 = ( (โˆ’1)/6 )(1/4) a4 = (โˆ’1)/24 Putting n = 5 in (1) a5 = ๐‘Ž_(5 โˆ’ 1 )/5 a5 = (a4โˆ’)/5 a5 = ((โˆ’1)/24)/5 a5 = ((โˆ’1)/24)(1/5) a5 = (โˆ’1)/120 Hence first five terms of the sequence are -1, (โˆ’1)/2, (โˆ’1)/6, (โˆ’1)/24, and (โˆ’1)/120. The corresponding series is (-1) + ((โˆ’1)/2) + ((โˆ’1)/6) + ((โˆ’1)/24) + ((โˆ’1)/120) +โ€ฆโ€ฆ

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