Question

Find the sum of the first 100 natural numbers.​

Answer 1

Answer:

we get

S100=1002[2×1+(100−1)×1]S100

=50[2+99]S100

=50×101S100

=5050

∴ The sum of first 100 natural numbers is 5050.

Answer 2

Let S be the required sum.

Therefore, S = 1 + 2 + 3 + 4 + 5 + ...+ 100

Clearly, it is an Arithmetic Progression whose first term = 1, last term = 100 and number of terms = 100.

Therefore, S = 100/2 (100 + 1), [Using the formula S = n/2(a + l)]

= 50(101)

= 5050

Therefore, the sum of first 100 natural numbers is 5050.

hope it helps..