Compute 1 + 2 + 3 + … + 9 8 + 9 9 + 1 0 0 .
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This is the lamest solution one could come up with.
that's the easiest formula
simple................
@Parth Lohomi you have 195 persons following you and you are level 5 in Algebra , Number Theory and in calculus . Posting questions like these is just not done................ And how did the problem managed to receive one like.
1 + 2 + 3 + . . . + 1 0 0
= ( 1 + 1 0 0 ) + ( 2 + 9 9 ) + ( 3 + 9 8 ) + . . . + ( 5 0 + 5 1 )
= 1 0 1 × 5 0
5 0 5 0
The sum of an Arithmetic Progression is
S = 2 n ( a 1 + a n ) = 2 1 0 0 ( 1 + 1 0 0 ) = 5 0 5 0
The answer is 2 1 0 0 × 1 0 1 = 5 0 × 1 0 1 = 5 0 5 0 .
∑ n = 1 1 0 0 n = 5 0 5 0
1 + 2 + 4 + ⋯ + n = 2 n ( n + 1 ) Setting n = 1 0 0 , this becomes: 1 + 2 + 3 + 4 + ⋯ + 1 0 0 = 2 1 0 0 ( 1 0 0 + 1 ) = 2 1 0 0 ( 1 0 1 ) = 5 0 ( 1 0 1 ) = 5 0 5 0
Sum of n terms formula of a.p =>Sn=n/2×(2a+(n-1)×d) where a=1, n=100, d=1, put all the values and get the answer
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We know that sum of (n) natural numbers is 2 n ( n + 1 )
so , 2 1 0 0 ( 1 0 1 ) = 5 0 5 0