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Asked by 20sanjaykoley20 | 19 Dec, 2023, 12:57: AM
Expert Answer
Each term in above sum is written as
Each term is arithmetic progression ( 4+7+10+........... ) . Number of terms in arithmetic progression (A.P.)equals term number .
For example first term of given sum has only one term of A.P. , second term of given sum fas two terms of A.P etc..
Given sum is written as
inner sum is written as
Hence in above sum , first term is sum of natural numbers and second term is sum of squares
Above expression is simplified as
Hence we get , S29 = (1/2) ( 29 × 30 × 32) and S9 = (1/2) ( 9 × 10 × 12)
S29 - S9 = 60 × [ 232 - 9 ]
(1/60) [ S29 - S9 ] = 223
Answered by Thiyagarajan K | 19 Dec, 2023, 11:53: AM
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