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