Question

What is
n + (n-1) + ......... + 1 = ?

And how?

Answer 1

the sum of all terms up to n th digit is n(n+1)/2

Answer 2

Answer: n(n+1)/2

This is the general method to prove the question

Step-by-step explanation:

⇒ In step 1 it’s your question just added “ S “ ( Sum )

⇒ In step 2 i have written it in opposite way .

⇒ Now we have to add both . That is in step 3 we are adding both ( 1 and 2 )

Now interesting thing comes here , you can see in the attachment that in step 2 -> 1 is written below n . 2 is written below n-1 . 3 is written below n-2 . 4 is written below n-3 . And so on ....... .

So when we will add these :- S + S = ( n+1 ) + ( n - 1 +2 ) + ( n -2 + 3 ) and so on ...... .

There is same term I.e = ( n + 1 ) + ( n +1 ) ............+ ( n + 1 )

⇒ These ( n + 1 ) is added “ n “ times So , 2S = n(n+1)

Rest you can see in attachment. Any queries ask in comment or Dm .

Hope It Helps You .