Let n>=1.
Prove by induction for all
n>=1 1+5+9+...+[4(n-1)+1]+[4n+1] = (n+1)(2n+1).

Proved

Step-by-step explanation:

Given

Required

Prove by induction

Increment n by 1 on both sides

Simplify the right hand side

Group the left hand side

Recall that

----[Given]

So; Substitute for on the left hand side

Open All Brackets

Collect Like Terms

Notice that the expression on both sides are equal;

Hence, the given expression has been proven

135 is your answer

step-by-step explanation:

try 180 times three then divide that number by 4 (sides) to get your answer. im glad to : )

the answer will be