Question

For the given statement Pn, write the statements P1, Pk, and Pk+1.

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

Answer 1

i already have P_n, and P_k, i need help with P_k+1

Answer 2

substitute n for k+1

Answer 3

okay so would it be 2k + 2(k+1) = k+1[(k+1) + 1] ?

Answer 4

hmm no remember on the last post
\[\rm 2+4+6+......+2k=\color{ReD}{k(k+1)}\]
we assumed n=k
you should use this assumption for the 3rd step

Answer 5

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Answer 6

\[\rm \color{orange}{2+4+6+......+2k}=\color{ReD}{k(k+1)}\]

n=k+1
\[\rm 2+4+6+......+2k +2(k+1)=\color{ReD}{(k+1)[(k+1)+1]}\]
as you can see `2+4+6....2k ` is equal to k(k+1)

Answer 7

we should keep this 2+4+6....2k at left side

Answer 8

p(k):2+4+ +2k = k(k+1)
p(k+1): 2+4+6-----+2k+ (2k+2)= k(k+1)+(2k+2)

Answer 9

is it clear

Answer 10

is it k(k+1) + 2k + 2(k+1) = k+1[(k+1)+1] ?

Answer 11

\[\rm \color{orange}{2+4+6+......+2k}=\color{ReD}{k(k+1)}\]
left side 2+4+....+2k(including) equal to k(k+1)
\[\rm \color{orange}{2+4+6+......+2k} +2(k+1)=\color{ReD}{(k+1)[(k+1)+1]}\]
so replace all the orange by k(k+1)