Question

Find out the sum of an ap 1+1+2++1+2+3+1+2+3+4........​

Answer 1

Answer:

Let's see what it is,

1+1+2+1+2+3+1+2+3+4+...

Or, 1+1+1+1...n times+ 2+2+2..n-1 times....

Or, n+ 2(n-1)+3(n-2)+... —————>(i)

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

3(n-2)-2(n-1)= n-4

And so on. So the difference is further decreasing by -2 in the give. series.

So if I write the series in such a way that the difference is n and then at last and then subtract the series 2,4,6... Then I get my answer right?

So the series becomes

n+2n+3n..-(2+4+6+...)

So it is (n/2)(2n+(n-1)n) - (n/2)(4+(n-1)2)

Ive used the formula sum of n terms.

Solve it and you'll get the answer

Nice question btw