Question

3 + 6 + 9 + ....+ 3n = 3n ( n + 1 ) / 2

Answer 1

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Answer 2

Answer:

3 + 6 + 9 + ....+ 3n = 3n ( n + 1 ) / 2

Step-by-step explanation:

1) Show this is true for 1: with n= 1, "3+ 6+ 9+ ...+ 3n" becomes just "3". What do you get setting n= 1 in 3n(n+1)/2?

2) Assume the statement is true for some "k" and prove it is true for "k+1".

If 3+ 6+ 9+ ...+ 3k= 3k(k+ 1)/2 then

3+ 6+ 9+ ...+ 3k+ 3(k+ 1)= (3+ 6+ 9+ ...+ 3k)+ 3(k+1)= 3k(k+1)/2+ 3(k+ 1).