Question

Sum the series: 1+3+7+15+31+............to n terms.

Answer 1

for solution refer attachment

nice question

Answer 2

Answer:

$2^{n+1}-n-2$

Step-by-step explanation:

$1+3+7+15+31+...........n terms$

$1+(2^{2}-1)+(2^{3}-1)+(2^{4}-1)+................(2^{n}-1)$

$1-(n-1)+2^{2}+2^{3}+2^{4}........2^{n}$

$1-n+1+\frac{2^{2}(1-2^{n-1})}{1-2}$   (using sum of finite geometric series)

$2-n+2^{2}(2^{n-1}-1)$

$2-n+2^{n+1}-2^{2}$

$2-n+2^{n+1}-4$

$2^{n+1}-n-2$

which is the required sum.