C-13-Q128mediumsingle_mcq

A man receives wages: $1$ paisa on day $1$ , $2$ paisa on day $2$ , $4$ paisa on day $3$ , doubling each day for $30$ days. His total wages (in paisa) is —

a $2^{30} - 1$
b $2^{30}$
c $2^{31} - 1$
d $30 \cdot 2^{29}$

ব্যাখ্যা

Daily wages form a geometric series $1+2+4+\cdots$ with $a=1,\ r=2$ over $30$ days. The total is $S_{30}=\dfrac{2^{30}-1}{2-1}=2^{30}-1$ .

এই অধ্যায়ের আরও প্রশ্ন

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Finite Series — সব প্রশ্ন দেখুন (160টি) →

A man receives wages: $1$ paisa on day $1$ , $2$ paisa on day $2$ , $4$ paisa on day $3$ , doubling each day for $30$ days. His total wages (in paisa) is —

2^{30} - 1

2^{30}

2^{31} - 1

30 \cdot 2^{29}

ব্যাখ্যা

Daily wages form a geometric series $1+2+4+\cdots$ with $a=1,\ r=2$ over $30$ days. The total is $S_{30}=\dfrac{2^{30}-1}{2-1}=2^{30}-1$ .

A man receives wages: 111 paisa on day 111, 222 paisa on day 222, 444 paisa on day 333, doubling each day for 303030 days. His total wages (in paisa) is —

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

A man receives wages: 111 paisa on day 111, 222 paisa on day 222, 444 paisa on day 333, doubling each day for 303030 days. His total wages (in paisa) is —

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

A man receives wages: $1$ paisa on day $1$ , $2$ paisa on day $2$ , $4$ paisa on day $3$ , doubling each day for $30$ days. His total wages (in paisa) is —

A man receives wages: $1$ paisa on day $1$ , $2$ paisa on day $2$ , $4$ paisa on day $3$ , doubling each day for $30$ days. His total wages (in paisa) is —