Sum of Series

Chapter 8 Class 11 Sequences and Series
Serial order wise

Transcript

Question 4 Find the sum to n terms of the series 1/(1 2) + 1/(2 3) + 1/(3 4) + nth term of series 1/(1 2) + 1/(2 3) + 1/(3 4) + is 1/( ( + 1)) an = 1/( ( + 1)) = (( + 1) )/( ( + 1)) = (( + 1))/( ( + 1)) /( ( + 1)) = 1/ 1/(( + 1)) Now, an = 1/ 1/(( + 1)) Adding all terms Sn = ("1 " " " 1/2) + (1/2 " " " " 1/3) + (1/3 " " " " 1/4) + +(1/( 1) " " " " 1/ )+ (1/ " " " " 1/( + 1)) Sn = 1 1/2 + 1/2 1/3 + 1/3 1/4 + + 1/( 1) " " " " 1/ + 1/ 1/( + 1) Sn = 1 1/( + 1) Sn = (( + 1) 1)/( + 1) Sn = ( + 1 1)/( + 1) Sn = ( + 0)/( + 1) Sn = /( + 1) Thus, the required sum is /( + 1)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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