Question

what is sum of first n natural numbers​

Answer 1

Answer:

n(n+1)/2.................

Answer 2

Answer:

n(n+1)

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2

Step-by-step explanation:

To find --->Sum of first n natural numbers

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Solution---> Natural numbers are the

--------------- collection of whole numbers starting with one in other words all whole numbers are natural number excluding 0.

So first n natural numbers are

1,2,3,4,5.....................,(n-1),n

now , a₂-a₁=2-1=1 , a₃-a₂=3-2=1

clearly a₃-a₂=a₂-a₁

So first n natural numbers form an AP

Now we have to find sum of first natural number

a =1 ,d =a₂-a₁=2-1=1 ,n=n , Sₙ=?

n

Sₙ= -----{ 2a + (n-1)d}

2

n

Sₙ=-----{2(1) +(n-1)(1)}

2

n n n(n+1)

=-----(2+n-1)= ---- (n+1)= -----------

2 2 2

Additional information--->

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1) 1²+2²+3²+..........+n²=n(n+1)(2n+1)/6

2)1³+2³+3³+...........+n³=n²(n+1)²/4