So here comes the easy one!

Algebra Level 1

Compute 1 + 2 + 3 + + 98 + 99 + 100. 1+2+3+\ldots+98+99+100.


The answer is 5050.

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7 solutions

Parth Lohomi
Sep 13, 2014

We know that sum of (n) natural numbers is n ( n + 1 ) 2 \dfrac{n(n+1)}{2}

so , 100 ( 101 ) 2 \dfrac{100(101)}{2} = 5050 \boxed{5050}

This is the lamest solution one could come up with.

John M. - 6 years, 8 months ago

that's the easiest formula

Varun Mishra - 6 years, 9 months ago

simple................

PUSHPESH KUMAR - 6 years, 8 months ago

@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.

Shubhendra Singh - 6 years, 9 months ago
Kartik Kulkarni
Jan 6, 2015

1 + 2 + 3 + . . . + 100 1 + 2 + 3 + ... + 100

= ( 1 + 100 ) + ( 2 + 99 ) + ( 3 + 98 ) + . . . + ( 50 + 51 ) = (1 + 100) + (2 + 99) + (3 + 98) + ... + (50 + 51)

= 101 × 50 = 101 \times 50

5050 \boxed {5050}

The sum of an Arithmetic Progression is

S = n 2 ( a 1 + a n ) = 100 2 ( 1 + 100 ) = 5050 S = \frac{n}{2}(a_{1} + a_{n}) = \frac{100}{2}(1+100) = 5050

Ashish Menon
May 31, 2016

The answer is 100 × 101 2 = 50 × 101 = 5050 \dfrac{100 × 101}{2} = 50 × 101 = \color{#69047E}{\boxed{5050}} .

Aryan Gaikwad
Apr 12, 2015

n = 1 100 n = 5050 \sum _{ n=1 }^{ 100 }{ n } = 5050

1 + 2 + 4 + + n = n ( n + 1 ) 2 1+2+4+\dotsm+n=\frac{n(n+1)}{2} Setting n = 100 n=100 , this becomes: 1 + 2 + 3 + 4 + + 100 = 100 ( 100 + 1 ) 2 = 100 ( 101 ) 2 = 50 ( 101 ) = 5050 1+2+3+4+\dotsm+100=\frac{100(100+1)}{2}=\frac{100(101)}{2}=50(101)=\boxed{5050}

Varun Mishra
Sep 13, 2014

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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