Prove that the ratio of the sum of ...

Prove that the ratio of the sum of m A.M.’s between any two numbers to the sum of n A.M's between the same numbers is equal to `m/n`.

Topper's Solved these Questions

PROGRESSION
KALYANI PUBLICATION|Exercise EXERCISE|249 Videos
MATHEMATICAL LOGIC
KALYANI PUBLICATION|Exercise EXERCISE|290 Videos
SYSTEM OF NUMERATION
KALYANI PUBLICATION|Exercise EXERCISE|101 Videos

Similar Questions

Explore conceptually related problems

Prove that the sum of n A.M.'s between any two numbers is equal to n times the A.M. of the two numbers.

Show that the sum of 500 A.M.’s between 2 and 3 is 1250.

Prove that the product of n G.M.’s between a and b is (ab)^(n/2)

Find the sum of first n even natural numbers.

Determine p A.M.’s between 1 and p^2 .

What is the inverse ratio of m:n?

Insert seven A.M.’s between 1 and 41.

Insert five G.M.’s between 3 and 192.

The product of two numbers is 16. The product of two A.M.’s between them is 24. Find the numbers.

Insert five G.M.'s between 8 and 1/8 .

KALYANI PUBLICATION-PROGRESSION-EXERCISE

By inserting eight A.M.’s between 2 and 29 prove that the sum of t...
Text Solution
|
Show that the sum of 500 A.M.’s between 2 and 3 is 1250.
Text Solution
|
Prove that the ratio of the sum of m A.M.’s between any two n...
Text Solution
|
The sum of fIrst n terms of an A.P series is 26n-2n^2. Find the fifth ...
Text Solution
|
Find the rth term of an A.P., the sum of whose first n terms is 2n+3n^...
Text Solution
|
The first term and common difference of an A.P. are 3 and 2 respective...
Text Solution
|
The fifth and ninth terms of an A.P. are respectively -15 an...
Text Solution
|
The first term and common difference of an A.P. are respectively 4 and...
Text Solution
|
The first term and common difference of an A.P. are respectively -2 an...
Text Solution
|
The first term and last term of an A.P. are respectively 1 and 157. If...
Text Solution
|
The first term and last term of an A.P. are 5 and 123 respectively. ...
Text Solution
|
If the sum upto 21st term of an A.P. is 630, determine the 11th ...
Text Solution
|
If 18th term of an A.P. is 52, determine the sum upto 35th term.
Text Solution
|
In an A.P. if the ratio of the sum upto 10th term and the 10th...
Text Solution
|
The seventh term of an A.P. is 20 and the sum of first twenty terms ...
Text Solution
|
The sum of first ten terms of an A.P. is 120. The sum of next ten term...
Text Solution
|
In an A.P. the ratio of 7th term to 11th term is 19 : 31 and the sum ...
Text Solution
|
The sum of first nine terms of an A.P. is 171 and that of 24 terms is ...
Text Solution
|
In an A.P. the nth term is p and the sum of first n terms is q. Show t...
Text Solution
|
If {S1,S2,S3} denoted the sum of n terms of three series in A.P. the f...
Text Solution
|