Question

What is the answer to the question?​

Answer 1

Explanation:

1+2+3+4+5+...n=n(n+1)/2

we Prove for the statement is true when n=1

l.h.s = r.h.s

1 = 1(1+1)/2 =>1

which is true

we assuming is true for n=k

we have:

1+2+3+4+5....k=k(k+1)/2

we proof for k=k+1

we have:

1+2+3+4+5+.....k+(k+1)=k+1((k+1)+1)/2

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

K(K+1)+2(K+1)/2=

K²+K+2K+2/2 = ↓

K²+3K+2 /2 =

(K+1)(K+2)/2 =(K+1)(K+2)/2

PROVED