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If for sequence lt a_n gtsum of n terms S_n= 2n^2+3n then find the sum {:(""Sigma Sigma),(1lei lt j le 10):}a_ia_j |
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Answer» `thereforea_(n)=S_(n)-S_(n-1)` `=2n^(2)+3n-2(n-1)^(2)-3(n-1)` =4n+1 Therefore, the sequence is 5,9,13… `thereforeunderset(1leiltjle10)(SigmaSigma)a_(i)a_(J)=(sum_(i=1)^(10)sum_(j=1)^(10)(4i+1)cdot(4j+1)-sum_(i=1)^(10)(4i+1)^(2))/2` `=((sum_(i=1)^(10)(4i+1))^(2)-sum_(i=1)^(10)(4i+1)^(2))/2` =23145 |
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