Golu was obese, and hence he decided to stick to a diet regime. On Monday, he ate half Paratha. He ate half of what was left on Tuesday and so on. He followed this pattern for one week. If, one Paratha amounts to 100 calories, then what is the calorie intake of Golu during the week (7 days)?

Given:

Golu ate half of his previous day's intake each day for a week (7 days)

Concept:

This constitutes a geometric series where each term is half of the previous term. s.

Calculation:

Summation of a G.P.\(= \frac{{a\left( {1 - {r^n}} \right)}}{{1 - r}}\)

Where a is starting term and r is multiplication factor.

Given, Golu ate half a Paratha on Monday he ate half of what was left on Tuesday and so on.

Amount of Paratha eaten by Golu \(= \frac{1}{2} + \frac{1}{2} \times \frac{1}{2} + \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \ldots \ldots ..\; + {\frac{1}{2}^7}\)

a = 1/2 

r = 1/2

n = 7

⇒ Amount of Paratha eaten by Golu \(= \frac{1}{2} \times \frac{{1 - \frac{1}{{{2^7}}}}}{{1 - \frac{1}{2}}}\)

⇒ Amount of Paratha eaten by Golu \(= \frac{1}{2} \times \frac{{1 - \frac{1}{{128}}}}{{\frac{1}{2}}} = \frac{{127}}{{128}} = 0.9922\)

∴ Amount of Paratha eaten by Golu in calories = 0.9922 x 100 = 99.22

∴ The total calorie intake of Golu during the week is approximately 99.22 Calories.