Question

1+2+3+-----+n=1/2 n(n+1) prove by methamatical indection¥ n>1

Answer 1

Step-by-step explanation:

To prove --->

--------------- n ( n +1)

1+2+3 + ----------- + n = -----------------

2

By mathematical induction

Proof--->

-----------

For n = 1

1 = 1 ( 1 + 1 )/ 2

= 1 ( 2 ) / 2

= 1

So given statement is true for n = 1

Let given statement is true for n= k

k ( k + 1)

1+ 2 +3 +.............. + k = ----------------

2

Adding ( k + 1 ) both sides

k(k+1)

1+2+3+....+ k + (k +1 ) = ----------- +(k+1)

2

k

= ( k + 1 ) ( ------ + 1)

2

= (k + 1 ) ( k + 2 / 2)

( k +1 ) ( k + 2 )

= ---------------------------

2

So given statement is true for n= k+1 if it is true for n= k

So by principle of mathematical induction given statement is true for all natural numbers