We will now show that two different rearrangements of the alternating harmonic series add up to two different values.
(1) Consider[infinity]∑k=1(−1)k+1k= 1−12+13−14+15−16+17−···In the PreLab you showed that this series converged by satisfying the hypotheses of the Alternating Series Test. Thus, we may use the Remainder in Alternating Series (Theorem 8.20 in the text) Theorem to bound the actual sumS.

(a) Note that the first partial sum, S1= 1.
(i) The Remainder in Alternating Series Theorem states that the actual sumS(of which we will not determinethe exact value here) satisfies|S−S1|<.
(ii) Using properties of absolute values< S−S1<
(iii) AddingS1= 11−< S <1 +(iv) We concludeS <

(b) We repeat the steps forS2=
(i) the actual sumSsatisfies|S−S2|<.
(ii) Using properties of absolute values< S−S2<
(iii) So,< S <(iv) We concludeS

i'm sure goog can you get that answer

10000

step-by-step explanation: divide by 2,

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week