Question

If n=10,12and 20,then prove that: 1+2+3+_+n=n(n+1)/2 choose some values for n. Is all follow of the above is true?​

Answer 1

Answer:

they will be true for any value of

n(principal quantum number)

Step-by-step explanation:

This is what I have done so far.

Show truth for N=1N=1

Left Hand Side = 1

Right Hand Side = 12(1)(1+1)=112(1)(1+1)=1

Suppose truth for N=kN=k

1+2+3+...+k=12k(k+1)1+2+3+...+k=12k(k+1)

Proof that the equation is true for N=k+1N=k+1

1+2+3+...+k+(k+1)1+2+3+...+k+(k+1)

Which is Equal To

12k(k+1)+(k+1)12k(k+1)+(k+1)

This is where I'm stuck, I don't know what else to do. The answer should be:

12(k+1)(k+1+1)12(k+1)(k+1+1)

Which is equal to:

12(k+1)(k+2)12(k+1)(k+2)

Right?

By the way sorry about the formatting, I'm still new.

if you like the answer then please kindly mark me as the brainliest