# EXERCISE 17.1

QUESTION 1

Evaluate the following :

(i)

Sol :

(ii)

Sol :

(iii)

Sol :

(iv)

Sol :

(v)

Sol :

= 31

QUESTION 2

If find the value of n

Sol :

Given :

QUESTION 3

If find

Sol :

Now,

= 66

QUESTION 4

If find

Sol :

We have,

Now

= 23

QUESTION 5

If find x

Sol :

QUESTION 6

If find x

Sol :

QUESTION 7

If find r

Sol :

QUESTION 8

If find r

Sol :

And

QUESTION 9

If find r

Sol :

We have,

QUESTION 10

If find n

Sol :

We have

QUESTION 11

If , find r

Sol :

We have

QUESTION 12

If and are in A.P. then find n

Sol :

Since and are in AP.

[ if a ,b ,c are in A.P then 2b=a+c ]

and 14

QUESTION 13

If find n

Sol :

Given :

or,

Now,

But this is not possible

QUESTION 14

If find

Sol :

Now ,

QUESTION 15

If then find the value of

Sol :

multiplying with 3 to numerator and denominator to make 4 :

QUESTION 16

Prove that the product of 2n consecutive negative integers is divisible by

Sol :

Let 2n negative integers be

Then, product

This is divisible by

[Alternate method]

Product

Hence

This is divisible by

QUESTION 17

For all positive integers n , show that

Sol :

LHS

RHS

QUESTION 18

Prove that:

Sol :

Hence , proved

QUESTION 19

Evaluate

Sol :

= 42504

QUESTION 20

Let and be positive integers such that . Then prove the following

(i)

Sol :

LHS

(ii)

Sol :

(iii)

Sol :

(iv)

Sol :

= R H S

Insert math as
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