Make an inductive conclusion about the nth term in following pattern, `1+2=(2*3)/2,1+2+3=(3*4)/2,1+2+3+4=(4*5)/2,...`



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Posted on (Answer #1)

Given the following pattern:


Find an expression for the `n^(th)` term:

We are adding the natural numbers from 1 to `n` ; the sum is seen to be equal to the product of `n` and `n+1` all divided by 2.


The inductive hypothesis is :

`1+2+3+***+n=(n(n+1))/2`  or `sum_1^n n=(n(n+1))/2`


This sums form a well-known sequence called the triangular numbers.


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