Question

Find the smallest integer n such that 1 + 2 + 3 + ... + n > 450.

Answer 1

there is a formula for left hand side :
1 + 2 + 3 +.... + n = n(n+1)/2

Answer 2

plug that in the given inequality,
it becomes to figure out wat n cud be..

Answer 3

n(n+1)/2 > 450

n(n+1) > 900

Answer 4

so product two consecutive numbers should give u > 450

do trial and error

Answer 5

is 29*30 > 900 ?
is 30*31 > 900 ?

yup corrected :P

Answer 6

Where did you get the formula?

Answer 7

http://lmgtfy.com/?q=sum+of+first+n+natural+numbers

Answer 8

@ganeshie8 I got it. Thank you!

Answer 9

in general ...

let A = 1 + 2 + 3 + ... + n-2 + n-1 + n

can be doubled and added together in a special way :)

A = 1 + 2 + 3 + ... + n-2 + n-1 + n
+A = n + n-1 + n-2 + ... + 3 + 2 + 1
--------------------------------------------
2A = n+1 + n+1 + n+1 + ... + n+1 + n+1 + n+1

so we have 2A = (n+1), n times.

A = n(n+1)/2