Example 14: Find the sum of
(i) the first 1000 positive integers
(ii) the first n positive integers
Answers
Answered by
136
To Find:
The sum of,
- The first 1000 positive integers.
- The first n positive integers.
We know that:
- Sₙ = {n(a + l)}/2
Where,
- Sₙ = Sum of nth term
- n = Number of terms
- a = First term
- l = Last term
Finding the sum of first 1000 positive integers:
1 + 2 + 3 + 4 + . . . . . . + 1000
We have,
- a = a₁ = 1
- l = n = 1000
S₁₀₀₀ = {1000(1 + 1000)}/2
S₁₀₀₀ = {1000 × 1001}/2
S₁₀₀₀ = 500 × 1001
S₁₀₀₀ = 500500
Hence,
- Sum of first 1000 positive integers = 500500
Finding the sum of first n positive integers:
1 + 2 + 3 + 4 + . . . . . . + n
We have,
- a = a₁ = 1
- l = n = n
Sₙ = {n(1 + n)}/2
Sₙ = {n + n²}/2
Hence,
- Sum of first n positive integers = {n + n²}/2
Answered by
125
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★ Step by step explanation :-
- Here, we have to find out the sum of first 1000 positive integers and the sum of first n positive integers.
★ Solving for first case :-
- AP = 1 + 2 + 3 . . . . . . + 1000
Therefore,
- n = 1000
- l = 1000
- a = 1
★ Using formula :-
★ Putting all known values :-
★ Solving for first case :-
- AP = 1 + 2 + 3 . . . . . . + n
Therefore,
- n = n
- l = n
- a = 1
★ Using formula :-
★ Putting all known values :-
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