Question

S = 2¹ +2² +2³ + ... + 2^n Паскаль​

Answer 1

1. uses Math;
2. var
3.  S: real;
4.  N, i: byte;
5. begin
6.  Write('Введите N: ');
7.  Read(N);
8.  for i := 1 to N do
9.    S := S + Power(2.0, i);
10.  Writeln('S = ', S);
11. end.

Answer 2

The expression you provided represents a sum of powers of 2, starting from 2^1 and going up to 2^n. This sum is often called a geometric series because each term is obtained by multiplying the previous term by a common ratio, in this case, 2.

The sum of a geometric series can be calculated using the formula:

S = a * (r^n - 1) / (r - 1),

where:

• S is the sum of the series,
• a is the first term of the series,
• r is the common ratio, and
• n is the number of terms in the series.

In this case, the first term (a) is 2^1 = 2, the common ratio (r) is 2, and we need to find the sum up to the nth term.

So, the sum of the series S = 2^1 + 2^2 + 2^3 + ... + 2^n is:

S = 2 * (2^n - 1) / (2 - 1) S = 2 * (2^n - 1)

Therefore, the sum of the series S = 2¹ + 2² + 2³ + ... + 2^n is 2 * (2^n - 1).