Series

The series of natural numbers is divided into groups (1),(2,3,4),(5,6,7,8,9)....and so on.
Find the sum of the numbers in the n^th group.

1 Answers

It can be observed that the last term of each bracket is the square of the natural number in which the serial of the bracket falls.

So the last term of the nth bracket = n² (if we start numbering the 1st bracket by 1)

also last bracket contains 2n-1 terms

so, last bracket after reversing would look like n², n²-1, n²-2,...... which is an AP whose sum = (2n-1 / 2)(2n²+(2n-1-1)(-1)) = (2n-1)(n²-n+1)

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