This is an infinite series with a common ratio of \( \frac{1}{7} \). We can write the series as: \[ 7 = 5 + \frac{1}{7} (5 + \alpha) + \frac{1}{7^2} (5 + 2\alpha) + \cdots. \] This is a geometric series. By setting up the sum of the series and solving for \( \alpha \), we find its value.
Final Answer: \( \alpha = \frac{6}{7} \).
\[ 5m \sum_{r=m}^{2m} T_r \text{ is equal to:} \]
0.1 mole of compound S will weigh ...... g, (given the molar mass in g mol\(^{-1}\) C = 12, H = 1, O = 16)
The molar mass of the water insoluble product formed from the fusion of chromite ore \(FeCr_2\text{O}_4\) with \(Na_2\text{CO}_3\) in presence of \(O_2\) is ....... g mol\(^{-1}\):
Given below are two statements:
Statement (I): The first ionization energy of Pb is greater than that of Sn.
Statement (II): The first ionization energy of Ge is greater than that of Si.
In light of the above statements, choose the correct answer from the options given below: