Ex- find the 20th value of the following sequence 1,4,7,10..... Solution : a₁ = 1 n = 20 d=3 an = a₁ + (n − 1) x d - = 1+ (201) x 3 = 58 series • Series is the sum of a sequence if {a}=0 is a sequence then the associated series is Σ an = ao+a₁ + a₂ + az +... i=0 EX:find the nth rule of the sequence set number 1- 1,-1,1,-1,1,-1,........ 2- 2,1/4,1/8,1/16,1/32,.... 3- -4,5,-6,7,-8,9,-10,.....

Q: 2n+1 3) Rewrite the series with a new index of summation k so that k = n+1. (n+4)(n+1)

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Q: 1) Make a change of variable so that the following series begins with k = 5. n i=2 (−1)²+1 (i-1)²

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Q: 3 5) Find a power series for X +

A: Let  f(x) = 3/(x+5)

Q: 4.) Find the sum of the convergent series 4 n(n + 2)

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Q: Σ=on + 5") (-1)" 5n Find the sum of this infinite Series Σ=on +

A: Here we have to find the sum of given infinite series

Q: A. Write the first five (5) terms of the given series: an 2. a1 = 2, an+1 = 1. an = coS 3 1+ an

A: In this question we have to find first five terms of the given series.

Q: Find the sum of 10th term of the series (1) + (5+5) + (5 +5 +5°) + (5 + 5° + 5 + 5° +5°) +..

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Q: The first four nonzero terms of the series of 開51 A. 1+r+r + B. 1--1- 128 * C. 1-r+2² -r 1024 1 D.…

A: We will use the knowledge of Taylor series expansion and Taylor polynomials to find the first 4…

Q: 5"x3n Find the sum of the series: >(-1)" n! n=0

A: see below the answer and calculation

Q: Find the sum of the series

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Q: (-1)*+1 is The series 2k = 1 2k

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Q: Use Leibniz's method to find the sum of the series 2² +9² +16² +23² + ... +72² Suggestion: This is…

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Q: (1) Find the summation of the series +++++

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Q: 3n-1-12 15. What is the sum of the series E, +00 Zn=1 6n-1 5 A. D. 5 C. B.

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Q: - "(a, +a,) ifoesn odi bat ot roielunlso oiriqg e oal S = 1-r 8 (1-r') Use and = 2 1-r and to find:…

A: Here the given series is a geometric series with common ratio greater than one. So we use the second…

Q: 1. a. List out the first four terms of the following series: > n(n – 1)a,nx"-2 = In%=2 b. Combine…

A: Solution of the problem as follows

Q: The first term of an arithmetic series is (2t + 1) where t > 0 The nth term of this arithmetic…

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Q: Find the nth term an of the given infinite series for which n = 1, 2, 3,... 1 12 1 9 + 1 10 + 1 11 +

A: Given

Q: 17. For a geometric series, What are the first three terms of the series if the first term is 3? 17

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Q: For the series 1 + 9 + 81 + 729 + … a1 =  r =  The sum of the first 6 terms, S6, =

A: Given that  For the series 1 + 9 + 81 + 729 + …a1 = r = The sum of the first 6 terms, S6,

Q: (-1)"2"+1 is The sum of the series 5.9n n=1 -4 (a) 1+ (b) 5 1+ -2 (c) 5 1 -2 (d) 5 1+ -4 (e) 45 (f)…

A: Find the value of series.

Q: find the sum of the series

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Q: 5. Find the nth partial sum for the arithmetic series below. (a) 5+12+19+26+33+ ... ; n= 12. (b)…

A: 5)a) 5+12+19+26+33+.....n=12We have to find sum for the arithmetic series.The formula is given…