Rewrite the series −1 + 8 - 27 + ... + 1000 using sigma notation. 10 Ο Ση 10 Ο Σ(-1)+1 αγ Ο Σ(-1) 20 Ο Σ(-1)*, 3

Q: For the series The sum= 8 Ma n = 1 4n find the sum.

A:

Q: Find the sum for the series 6+ 2+ + + 3 6561

A: It is a geometric series with, Now let be the nth term of the given series. Then,

Q: Find the sum of the series. Σ 5(-1)"72n + 1 32n + 1(2n + 1)! n = 0

A:

Q: Write the series using summation notation. -3 + 4 - 5+6-7 Σ i i=1

A: Given series is Let the nth term of the series is  then, In general, for n=1,2,3,4,5, we have

Q: Q9. Consider the following algorithm: sum = 0 For j starting at 1 and ending with 15: sum = sum +…

A: We have to solve given problems:

Q: cn? Let c be a nonzero real number and a, = Which one of the following statements is correct? 26n? –…

A: Series is divergent

Q: (10k - 12)- (7 – 4n) x > (-6m) | 22.Evaluate the given series k=3 n=2 m=1 O A. -108 O B. -52 O C.…

A:

Q: Evaluate the infinite series described 1020 256 64 16 625 125 25 5 00 n - 1 +096· 4, n= 1 i – 1 4) 1

A: For a geometric progression, a+ar+ar2+ar3....., the common ratio, r is defined as the ratio of an to…

Q: Use the table of frequently used Taylor series to find the sum of the series. 2 3 4 5 X -X +X -X…

A:

Q: There are infinitely many series whose first two terms are 1/5 , 1/15 . Give three examples. You…

A: (a)  1.15,115,145,1135,14052.15,115,125,135,1453.15,115,15,115,15

Q: 13. 2 - 6 + 18 – 54 + 162 - 486

A: Solve

Q: Consider the series Find formulas for an and bn, where 3" + (-2)" Σ 11" n=1 Σ n=1 an = bn 3" + (-2)"…

A:

Q: (ii) 8 ΣΕ n=1 X

A: To find the sum of the following series.

Q: n=1 ,2n TO

A:

Q: 8. The series 133n en is and ---- n2 + 1 n = 0

A: The given series is 133nen/(n2+1).