Find four numbers forming a geometric progression in which third term is greater than the first term by 9, and the second term is greater than the 4 th by 18. If a, b, c and d are in G.P. show …

Oct 27, 2024 · For instance, for N = 9 + 99 + 999, the sum of digits would be 9 + 18 + 27, totaling 54, which follows the same concept of summing the occurrences of the digit 9.

To evaluate the expression 9+99+999+… up to n terms, we can follow these steps: - Continuing this pattern, the k -th term can be expressed as 10k−1. Here, n is subtracted because we have …

Mar 18, 2025 · This C program calculates and displays the sum of a series where each term is formed by repeating the digit 9 (e.g., 9, 99, 999, 9999, ...). The program prompts the user for …

By formula, Sum of G.P. = \dfrac {a (r^n - 1)} {r - 1} r −1a(rn − 1) \Rightarrow \dfrac {10 (10^n - 1)} {10 - 1} + (-n) \\ [1em] \Rightarrow \dfrac {10 (10^n - 1)} {9} - n. ⇒ 10− 110(10n − 1) +(−n) ⇒ …

To calculate the sum of the series: 9 + 99 + 999 + 9999 + ... + 999999999 (the last term with nine digits of 9), we can express the terms in a simplified way. Each term can be rewritten using …

Sep 9, 2023 · For example, if we take the sum of the first three numbers, 9, 99, and 999: 9 contributes 1, 99 contributes 2 (forming 1 and 1), and 999 contributes 3 (forming 1, 1, and 1).

The sum of the first 'n' terms of this series can be calculated using the formula: Sn = 10/81 * [ (99n - 9n) + 9]. These kind of series are referred as geometric series. In a geometric series each …

Dec 30, 2020 · (a) 10 9 10 9 (10100 – 1) – 100 Let S100 = 9 + 99 + 999 + ...... upto 100 terms = (10 – 1) + (100 – 1) + (1000 – 1) + ..... + upto 100 terms = (10 + 102 + 103 + .... upto 100 …

Dec 20, 2017 · 9 + 99 + 999 + 9999 + ............. So, For finding the sum of the given series, we can write the series as, = (10 - 1) + (100 - 1) + (1000 - 1) + .............. = (10 - 1) + (10² - 1) + (10³ - …