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