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. The Sum of an Infinite Geometric Series 3 We want to find out the sum of an infinite geometric series of the following x d form e S = a + a.r + a.r + a.r + ...... + a.r + ..... +·¥ p where a and r are real numbers and 0 < r < 1. To compute the sum, multiply A the above equation by r to obtain r.S = a.r + a.r + a.r + ...... + a·+ ..... +· ¥ Subtract the second equation from the first to get S – r.S = a or, (1 – r)S = a which yields a S = 1–r In the example used for the derivation of the money multiplier, a = 1 and r = 0.4. Hence the value of the infinite series is 1 5 1– 0.4= 3 Money Supply in India . 3 Table 3.4: Changes in M1 and M3 Over Time (in crore) (2023-24) x Year M1 M3 d (Narrow Money) (Broad Money) e 1999–00 341796 1124174 A 2000–01 379433 1313204 2001–02 422824 1498336 2002–03 473558 1717936 2003–04 578694 2005654 2004–05 649766 2245653 2005–06 826389 2719493 51 2006–07 967925 3310038 M n 2007–08 1155810 4017855 y 2008–09 1259671 4794775 d 2009–10 1489268 5602698 B n 2010–11 1638345 6504116 n 2011–12 1737394 7384831 g 2012–13 1897526 8389819 2013–14 2059762 9517386 2014–15 2292404 10550168 2015–16 2602538 11617615 2016–17 2681957 12791940 2017–18 3267331 13962587 2018–19 3710464 15432067 2019–20 4125948 16799963 2020–21 4794299 18844578 2021–22 5307125 20493129 2022–23 5674795 22343760 2023–24 6091700 24939860 2024–25 6584081 27286589 Source: Handbook of Statistics on Indian Economy, Reserve Bank of India, 2024–25 The difference in values between the two columns is attributable to the time deposits held by commercial banks. Reprint 2026-27