Question

Find the sum of all even natural numbers less than 200

Answer 1

Answer:

6534

Step-by-step explanation:

Sum of even the integers less than 200 and which are not divided by 6.

S

1

=2+4+6+8....+198

S

2

=6+12+36...198

_____________________

S

1

−S

2

=2(1+2+3....99)−6(1+2+....33)

=2(

2

99×100

)−6(

2

33×34

) [∵ sum of first 'n' natural numbers =

2

n(n+1)

]

=9900−3(33×34)

=9900−3366

⇒9900−3366

∴S

1

−S

2

=6534.

Answer 2

Step-by-step explanation:

Sum of even positive integers less than 200=>2+4+6+8... 198. 198 is the99th term of the series. required sum=(1)-(2)=6534