Question

In using induction to prove that the sum of the first n terms where
an = (4n − 3) is n(4n − 3)/2, what would be the mathematical expression
represented by Sk + ak + 1?

k(4k − 2)/2+ 4k − 3


k(4k − 2)/2+ 4k − 4


k(4k − 2)/2+ 4k + 1


(4k − 2)/2 + 4k − 3

Answer 1

to me, it is not the correct notation. How to prove?
We have to use induction to prove \(\sum_{n}^{\infty}4n-3= \dfrac{n(4n-3)}{2}\)
at n=1 , the left hand side is 4*1-3=1
while the right hand side is \(\dfrac{1*(4*1-3)}{2}=\dfrac{1}{2}\)
they are not equal.!!!