Question

2+4+6----+2n=n(n+1)​

Answer 1

For k: 2+4+6+8+.......+2k=k (k+1) ......(1)

To prove: For (k+1): 2+4+6+8+...+2(k+1)=(k+1)(k+2)......(2)

Proof:-

2+4+6+8+....+2k+2(k+1)

From (1)

K (k+1)+2(k+1)

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

From (2)&(3)

It'seems clear that p (k+1) is suitable for the given condition.

Hence by PMI given condition is true for all n belongs to N

Answer 2

Answer:

2+4+6+...+2n=2∗(1+2+3+...+n)=2n∗(n+1)2=n∗(n+1)2+4+6+...+2n=2∗(1+2+3+...+n)=2n∗(n+1)2=n∗(n+1)

दूसरा। मान लीजिए कि यह सच है, आपके पास है2+4+6+...+2n=n∗(n+1)2+4+6+...+2n=n∗(n+1) ये है S(n)S(n) दोनों पक्षों में 2 (n + 1) जोड़ें, दे रहे हैं

2+4+...+2n+2(n+1)=n∗(n+1)+2(n+1)=(n+2)(n+1)

2+4+...+2n+2(n+1)=n∗(n+1)+2(n+1)=(n+2)(n+1)