Question

"For the given statement Pn, write the statements P1, Pk, and Pk+1."
2 + 4 + 6 + . . . + 2n = n(n+1)

Could someone show me how to do this problem?

Answer 1

@ganeshie8 will you be able to help me?

Answer 2

P1-->n=1 .2=1*2
Pk-->n=k 2+4+6+...+2k=k(k+1)
pK+1--> n=k+1 2+4+6+8+...+2k+2(k+1)=(k+1)(k+2)
then we should show that, if the proposition is true for an arbitrary number k,
then it must be true for the next number:k+1
2+4+6+...+2k+(2k+2)=k^2+k+2k+2=k^2+3k+2=(k+1)(k+2)
so we proved that if we add 2(k+1) to HYPOTHESIS we can prove that 2+4+6+8+...+2k+2(k+1)=(k+1)(k+2)