Question

Solve: [1+ 1/(1*2) + 1/(1*2*4) + 1/(1*2*4*8) + 1/(1*2*4*8*16)]

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no direct answer need 2 simplification

Answer 1

Step-by-step explanation:

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1+1/2+1/8+1/64+1/1024

=1.6416015625

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Answer 2

☯To FinD :

We have to find the value of : $\large{\sf{ 1 + \frac{1}{1 \times 2} + \frac{1}{1 \times 2 \times 4} + \frac{1}{1 \times 2 \times 4 \times 8} + \frac{1}{1 \times 2 \times 4 \times 8 \times 16}}}$

$\rule{200}{1}$

☯ SolutioN :

Firstly, we will multiply the numbers which are in denominator.

$\sf{\dashrightarrow 1 + \frac{1}{1 \times 2} + \frac{1}{1 \times 2 \times 4} + \frac{1}{1 \times 2 \times 4 \times 8} + \frac{1}{1 \times 2 \times 4 \times 8 \times 16}} \\ \\ \sf{\dashrightarrow 1 + \frac{1}{ 2} + \frac{1}{ 2 \times 4} + \frac{1}{ 2 \times 4 \times 8} + \frac{1}{ 2 \times 4 \times 8 \times 16}} \\ \\ \sf{\dashrightarrow 1 + \frac{1}{2} + \frac{1}{8} + \frac{1}{8 \times 8} + \frac{1}{8 \times 8 \times 16}} \\ \\ \sf{\dashrightarrow 1 + \frac{1}{2} + \frac{1}{8} + \frac{1}{64} + \frac{1}{64 \times 16}} \\ \\ \sf{\dashrightarrow 1 + \frac{1}{2} + \frac{1}{8} + \frac{1}{64} + \frac{1}{1024}}$

↪Now, we will take LCM

$\sf{\dashrightarrow \frac{1024 + 512 + 128 + 16 + 1}{1024}} \\ \\ \sf{\dashrightarrow \frac{1681}{1024}} \\ \\ \sf{\dashrightarrow 1.64} \\ \\ \Large{\implies{\boxed{\boxed{\sf{1.64}}}}}$

$\therefore$ 1.64 is the required answer.