Question

P=(x+1)2*(x+1)3*(x+1)4*...*(x+1)n

Answer 1

Р=1+1*2*1*1+1*4=х+1n
p=20+1+1n
p=22n

Answer 2

The expression you provided is:

P = (x + 1)^2 * (x + 1)^3 * (x + 1)^4 * ... * (x + 1)^n

To simplify this expression, you can use the properties of exponents. When multiplying expressions with the same base, you can add the exponents. Therefore, you can rewrite the expression as:

P = (x + 1)^(2 + 3 + 4 + ... + n)

The sum of the exponents from 2 to n is the sum of an arithmetic series. The sum of an arithmetic series can be calculated using the formula:

S = (n/2) * (first term + last term)

In this case, the first term is 2, and the last term is n. So, the sum of the exponents can be written as:

S = (n/2) * (2 + n)

Substituting this value back into the expression, we have:

P = (x + 1)^(n/2 * (2 + n))

Therefore, the simplified expression for P is (x + 1)^(n/2 * (2 + n)).