the sum of the first n natural number is
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the sum of the first n natural number is
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Answer:
Sum of the First n Natural Numbers
We prove the formula 1+ 2+ ... + n = n(n+1) / 2, for n a natural number. There is a simple applet showing the essence of the inductive proof of this result.
Step-by-step explanation:
S
n
=1+2+3+....+n
S
n
=
2
n
[2a+(n−1)d] where a=1,d=2−1=1
⇒S
n
=
2
n
[2×1+(n−1)1]
⇒S
n
=
2
n
(n+1)
∴ Sum of first n natural numbers=
2
n(n+1)