Consider a series formed by deleting all terms from the harmonic series that contain the digit...
Consider a series formed by deleting all terms from the harmonic series that contain the digit 7. Show, with clear explanation of each step, that this series converges.
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Consider a series formed by deleting all terms from the harmonic
series that contain the digit...
please help with b) and c) Thank you:) (a) The harmonic series diverges very slowly. Prove...
please help with b) and c)
Thank you:)
(a) The harmonic series diverges very slowly. Prove that the sum of the first 106 terms is less than 15 and that the sum of the first 10° terms is less than 22. (You should not actually calculate these sums!) [2 marks] (b) Determine whether the series 10n +1 101 is convergent or divergent. [3 marks] (c) Consider the series whose terms are the reciprocals of the positive integers whose decimal represen-...
3. Consider the Cantor set D formed by deleting the middle subinterval of length 4-* from each re...
3. Consider the Cantor set D formed by deleting the middle subinterval of length 4-* from each remaining interval at step k. (a) Prove that the length of the D is 1/2. Thus D is a fat fractal. (b) What is the box-counting dimension of D? (c) Let be the function of [0,1] which is equal to 1 on D and 0 elsewhere. It is the limit of functions which are Riemann integrable. Note that f is not Riemann integrable....
Consider the number 35964 How many 3 digit numbers can be formed using digits from 35964...
Consider the number 35964 How many 3 digit numbers can be formed using digits from 35964 if no digits may be repeated? What is the sum on all of those 3 digit numbers?
Let S be the set of all 7-digit numbers which do not contain 0 in any...
Let S be the set of all 7-digit numbers which do not contain 0 in any place — that is, each element of S is a string of 7 digits with each digit chosen from the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. How many elements of S are there that don’t contain the substring 123? To qualify as having 123 as a substring, the numbers 1, 2 and 3 must appear in order and consecutively. For...
Mathematical Proofs Please show all work + I SHOW THE HARMonic SERIES I + 5 +...
Mathematical Proofs
Please show all work
+ I SHOW THE HARMonic SERIES I + 5 + 5 + 5 + 5 + + + + + + ... DIVERGES BY GROUPING TERMS APPROPRIATELY.
Please answer all parts. (1 point) Series: A Series (Or Infinite Series) is obtained from a sequence by adding the term...
Please answer all parts.
(1 point) Series: A Series (Or Infinite Series) is obtained from a sequence by adding the terms of the sequence. Another sequence associated with the series is the sequence of partial sums. A series converges if its sequence of partial sums converges. The sum of the series is the limit of the sequence of partial sums For example, consider the geometric series defined by the sequence Then the n-th partial sum Sn is given by tl...
7 Harmonic oscillator in "energy space" Consider the harmonic oscillator in "energy space", i.e., in terms...
7 Harmonic oscillator in "energy space" Consider the harmonic oscillator in "energy space", i.e., in terms of the basis of eigenvectors n) of the harmonic oscillator Hamiltonian, with Hn) -hwn1/2)]n). We computed these in terms of wavefunctions in position space, ie. pn(x)-(zln), but we can also work purely in terms of the abstract energy eigenvectors in Dirac notation. PS9.pdf 1. You computed the matrix elements 〈nleln) on an earlier problem set. Now find (nn) for general n,n' 2. Find the...
How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5,...
How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, and 7 if each digit can be used only once, how many are greater than 330
1. (a) (i) How many different six-digit natural numbers may be formed from the digits 2,...
1. (a) (i) How many different six-digit natural numbers may be formed from the digits 2, 3, 4, 5, 7 and 9 if digits may not be repeated? (ii) How many of the numbers so formed are even? (iii) How many of the numbers formed are divisible by 3? (iv) How many of the numbers formed are less than 700,000? (b) JACK MURPHY’s seven character password consists of four let- ters chosen from the ten letters in his name (all...
Show your calculations. (2 marks) How many five-digit numbers can be formed from the set of...
Show your calculations. (2 marks) How many five-digit numbers can be formed from the set of nine number 3, 4, 5, 6, 7, 8} if no number is repeated and no number starts with a zero, and a) there are no other restrictions? (2 marks) b) the result must be an odd number? (3 marks) Show your calculations. (5 marks total)
please help with b) and c)
Thank you:)
(a) The harmonic series diverges very slowly. Prove that the sum of the first 106 terms is less than 15 and that the sum of the first 10° terms is less than 22. (You should not actually calculate these sums!) [2 marks] (b) Determine whether the series 10n +1 101 is convergent or divergent. [3 marks] (c) Consider the series whose terms are the reciprocals of the positive integers whose decimal represen-...
3. Consider the Cantor set D formed by deleting the middle subinterval of length 4-* from each remaining interval at step k. (a) Prove that the length of the D is 1/2. Thus D is a fat fractal. (b) What is the box-counting dimension of D? (c) Let be the function of [0,1] which is equal to 1 on D and 0 elsewhere. It is the limit of functions which are Riemann integrable. Note that f is not Riemann integrable....
Mathematical Proofs
Please show all work
+ I SHOW THE HARMonic SERIES I + 5 + 5 + 5 + 5 + + + + + + ... DIVERGES BY GROUPING TERMS APPROPRIATELY.
Please answer all parts.
(1 point) Series: A Series (Or Infinite Series) is obtained from a sequence by adding the terms of the sequence. Another sequence associated with the series is the sequence of partial sums. A series converges if its sequence of partial sums converges. The sum of the series is the limit of the sequence of partial sums For example, consider the geometric series defined by the sequence Then the n-th partial sum Sn is given by tl...
7 Harmonic oscillator in "energy space" Consider the harmonic oscillator in "energy space", i.e., in terms of the basis of eigenvectors n) of the harmonic oscillator Hamiltonian, with Hn) -hwn1/2)]n). We computed these in terms of wavefunctions in position space, ie. pn(x)-(zln), but we can also work purely in terms of the abstract energy eigenvectors in Dirac notation. PS9.pdf 1. You computed the matrix elements 〈nleln) on an earlier problem set. Now find (nn) for general n,n' 2. Find the...
Show your calculations. (2 marks) How many five-digit numbers can be formed from the set of nine number 3, 4, 5, 6, 7, 8} if no number is repeated and no number starts with a zero, and a) there are no other restrictions? (2 marks) b) the result must be an odd number? (3 marks) Show your calculations. (5 marks total)
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