Question

for the given statement on Pn write the statements P1 Pk and Pk+1
2 + 4 + 6 + .... +2n = n(n+1)

Answer 1

P1=1(1+1)=2
for Pk substitute n=k on both sides
and then add 2(k+1) on both sides to get Pk+1

Answer 2

@surjithayer so Pk would be what? I'm not sure what I plug in for it and where

Answer 3

Pk is 2+4+6+...+2k=k(k+1)

Answer 4

@surjithayer then do I solve for K?

Answer 5

k is a general placeholder ... we know that for k=1, this holds

if it holds for some k, then does it hold for k+1? is what we need to prove. but thats not what this is asking is it

Answer 6

add 2(k+1) to both sides and simplify the right side to see if its of the form:

(k+1) (k+1+1)

Answer 7

So P1= 1(1+1)=2
Pk= 2+4+6+...+2k=k(k+1)
Pk+1= 2+4+6+...+2(k+1)=k+1((k+1)+1) ?????