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Question 1 - Finding sum from nth number - Chapter 8 Class 11 Sequences and Series
Last updated at April 16, 2024 by Teachoo
Chapter 8 Class 11 Sequences and Series
Concept wise
- Finding Sequences
- Arithmetic Progression (AP): Formulae based
- Arithmetic Progression (AP): Statement
- Arithmetic Progression (AP): Calculation based/Proofs
- Inserting AP between two numbers
- Arithmetic Mean (AM)
- Geometric Progression(GP): Formulae based
- Geometric Progression(GP): Statement
- Geometric Progression(GP): Calculation based/Proofs
- Inserting GP between two numbers
- Geometric Mean (GM)
- AM and GM (Arithmetic Mean And Geometric mean)
- AP and GP mix questions
- Finding sum from series
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Finding sum from nth number
Transcript
Question 1 Find the sum to n terms of the series 1 2 + 2 3 + 3 4 + 4 5 + Step 1: Find nth term (an) Here, an = n ( n + 1) = n2 + n Step 2: Finding sum of n terms = (n(n+1)(2n+1))/6 + (n(n+1))/2 = (n(n+1))/2 (((2n+1))/3 " + 1" ) = (n(n+1))/2 ((2n + 1 +3)/3) = (n(n+1))/2 ((2n + 4)/3) = n(n+1)/(2 3) [2(n + 2)] = (2n(n + 1)(n + 2))/6 Thus, the required sum is (2n(n + 1)(n + 2))/6
