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Chapter 12: Q 98. (page 811)

Show that

1+2+...+n-1+n=nn+12

Short Answer

Expert verified

It is shown that1+2+...+n-1+n=nn+12.

Step by step solution

01

Step 1. Write the given information.

The given information is:

1+2+...+n-1+n=nn+12

We have to prove that 1+2+...+n-1+nis equal to nn+12.

02

Step 2. Prove the given equation.

Let's take:

S=1+2+3+4+...+n-1+n鈥�1

We can also write it as:

S=n+n-1+...+4+3+2+1鈰�2

Now add both the equations,

S+S=1+2+3+4+...+n-1+n+n+n-1+...+4+3+2+12S=n+1+n-1+2+...+n-1+2+n+12S=n+1+n+1+...+n+12S=n+1路nS=n+1n2

Therefore, we can say that1+2+...+n-1+n=nn+12.

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