The value of `1-(1)/(20)+(1)/(20^(2))-(1)/(20^(3))+`....... till 5th term is

Options

A. `1.05`
B. `0.95238`
C. `0.95239`
D. `10.5`

Answer

To solve the expression \( 1 - \frac{1}{20} + \frac{1}{20^2} - \frac{1}{20^3} + \frac{1}{20^4} \) up to the 5th term, we can follow these steps:

### Step 1: Write down the expression
The expression we need to evaluate is:
\[ 1 - \frac{1}{20} + \frac{1}{20^2} - \frac{1}{20^3} + \frac{1}{20^4} \]

### Step 2: Calculate each term
- The first term is \( 1 \).
- The second term is \( -\frac{1}{20} = -0.05 \).
- The third term is \( \frac{1}{20^2} = \frac{1}{400} = 0.0025 \).
- The fourth term is \( -\frac{1}{20^3} = -\frac{1}{8000} = -0.000125 \).
- The fifth term is \( \frac{1}{20^4} = \frac{1}{160000} = 0.00000625 \).

### Step 3: Combine the terms
Now, we will combine these terms:
\[ 1 - 0.05 + 0.0025 - 0.000125 + 0.00000625 \]

### Step 4: Perform the addition and subtraction
1. Start with \( 1 \):
\[ 1 - 0.05 = 0.95 \]
2. Add \( 0.0025 \):
\[ 0.95 + 0.0025 = 0.9525 \]
3. Subtract \( 0.000125 \):
\[ 0.9525 - 0.000125 = 0.952375 \]
4. Finally, add \( 0.00000625 \):
\[ 0.952375 + 0.00000625 = 0.95238125 \]

### Step 5: Round to a suitable decimal place
Rounding \( 0.95238125 \) to five decimal places gives us:
\[ 0.95238 \]

### Final Answer
The value of the expression up to the 5th term is approximately:
\[ \boxed{0.95238} \]