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,...`

Topic:

Math

Asked on

1 Answer | Add Yours

embizze's profile pic

Posted on

Given the following pattern:

`1+2=(2*3)/2,1+2+3=(3*4)/2,1+2+3+4=(4*5)/2,...`

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.

Sources:

We’ve answered 301,523 questions. We can answer yours, too.

Ask a question