NCERT Class 11-Math's: Chapter –9 Sequence and Series Part 10

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Question 11:

Find the sum of the series

to (i) terms (ii) terms

Answer:

(i)

(ii)

Question 12:

Find the term of an A.P. sum of whose first terms is .

Answer:

Long Answer Type

Question 13:

If A is the arithmetic mean and , be two geometric means between any two numbers, then prove that

Answer:

Let the two numbers be ‘a’ and ‘b’

The arithmetic mean is given by and the geometric mean is given by

We have to insert two geometric means between a and b

Now that we have the terms

will be the geometric mean of a and and will be the geometric mean of and b

Hence and

Square

Put

Square both sides

Put value of in

Now we have to prove that

Consider RHS

Substitute values of and from (i) and (ii)

Divide and multiply by

But

Hence

Hence RHS=LHS

Hence proved