Question

Q11. What will be the sum of all possible values of l and m for n = 5 ? ​

Answer 1

If n=5

I=0 m=0

I=1  m= -1,0,1

I=2 m=-2,-1,0,1,2

I=3  m= -3,-2,-1,0,1,2,3

I=4 m=-4,-3,-2,-1,0,1,2,3,4,5

I=5    m=-5,-4,-3,-2,-1,0,1,2,3,4,5

Answer 2

Given:

n = 5  

To find:

Sum of all possible values of l and m

Solution:

Since the value of n is 5. Therefore, the value of l ranges from numerals 0 to 4.

Therefore, possible values of l = 0,1,2,3 and 4

Now,

For any value of l, the value of n ranges from -l to +l. Thus, it can range from - 4 to + 4.

Therefore, possible values of m = -4,-3,-2,-1,0,1,2,3 and 4

Sum of values of l -

= 0 + 1 + 2 + 3 + 4

= 10

Similarly,

Sum of values of m -

(-4) + (-3) + (-2) + (-1) + 0 + 1 + 2 + 3 + 4

- 10 + 10

= 0

Combining the value of both l and m -

= 10 + 0

= 10

Answer: Sum of all possible values of l and m is 10.