Start with the following simple equation: a=b (step 1) Multiply both sides by b: ab=b2 (step 2) Subtract a2 from both sides and factorize: ab−a2=b2−a2 (step 3) a(b−a)=(b+a)(b−a) (step 4) Simplify and add 1 to both sides: a=b+a (step 5) a+1=b+a+1 Now since a=b (the starting point of this proof), we can write this as: a+1=2a+1 And in the case where a=1, we have: 1+1=2+1 So, therefore, 1+1=3

b. astronomers

4444444444444 i think

whatare you sayig

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for