Question

FIND THE SUM OF ALL NATURAL NUMBERS BETWEEN 1000 AND 10000?

Answer 1

Hi ,

1001 , 1002 , 1003 , ........, 9999 are natural numbers between 1000 to

10000

***************************************************************************

The number of natural numbers between a and b where a < b is

b - a - 1

**************************************************************************

According to the problem,

a = 1001 ,

b = 9999,

Number of natural numbers between 1001 and 9999

n= 9999 - 1001 - 1

n= 8997

Sum of all natural numbers betwèen 1000 and 10000

Sn = n/2 [ a + b ]

S8997 = 8997/2 [ 1001 + 9999 ]

= 8997 /2 × ( 11000 )

= 49483500

I hope this will useful to you.

*****

Answer 2

1001,1002,1003........9999 are the natural number

a=1001

a=1

an=9999

a+(n-1)d=9999

1001+(n-1)d=9999

(n-1)=9999-1001

(n-1)=8998

n=8999

an=n\2[2a+(n-1)d]

S8999=4499.5(2002+8998)

S8999=4498.5*11000

S8999=49494500