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If `S_(n)` denotes sum of first `n` tem of a series and if `S_(n+2)-S_(n)=n^(2)` then `S_(20)` is `("given that" T_(1)+T_(2)=0)`A. `1540`B. `1140`C. `770`D. `1120` |
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Answer» Correct Answer - B If `S_(n)` denotes ………… `S_(n+2)-S_(n)=n^(2)` `T_(n+2)+T_(n+1)=n^(2)` `T_(1)+T_(2)=0` `T_(3)+T_(2)=1` `T_(4)+T_(3)=4` `T_(5)+T_(4)=9` and so on Now sequence is `T_(1), -T_(1), 1+T_(1),3-T_(1),6+T_(1),10-T_(1)`............. `i.e. S_(20) = T_(1)-T_(2)+1+3+6+10+` ....... up to 20 terms `S_(20 = 1+3+6+10+` ......... up 18 terms `S_(20) = sum_(r=1)^(18)(r^(2))/(2)+(r )/(2)` `S_(20) = 1140`. |
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