A number theory problem by Lakshay Gulati
Find the value of X. .. X=1+2+3+4+5.........+95+96+97+98+99+100
The answer is 5050.
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5 solutions
Most of us here know the formula T n = 2 n ( n + 1 ) , but here's how Gauss supposedly solved it extremely fast as a child:
x = 1 + 2 + . . . + 1 0 0 = ( 1 + 1 0 0 ) + ( 2 + 9 9 ) + . . . + ( 5 0 + 5 1 ) = 1 0 1 × 5 0 = 5 0 5 0
We may use n/2(2a+(n-2)d) since it forms an arithmatic series
How about using L A T E X in your solutions ?Also there's a slight error in your solution , I've corrected it .
Copy it off my comment ⌣ ¨
2 n ( 2 a + ( n − 1 ) d )
We can use the formula - n×(n+1)÷2
Try using L A T E X in your solutions and questions to make it look good ⌣ ¨
Your question : Find X= 1 + 2 + 3 + ⋯ + 1 0 0
Your answer : We can use the formula - 2 n ( n + 1 )
If you want , you can copy the L A T E X off my comment and edit your question and solution ⌣ ¨
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You've said it twice so I have to ask... What's latex?
Since sum of n natural numbers(starting from 1) is given by n(n+1)/2
here we get,
1+100=101
2+99=101
3+98=101 . . . .
so, we just need to add 101, 50 times i.e, 5050