Questions
The sum of the series to n terms is
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a
nn2+1n2+n+1
b
n(n+1)2n2+n+1
c
nn2−12n2+n+1
d
None of these
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Correct option is B
Given series is 11+12+14+21+22+24+31+32+34+…+ntermsIet T4 be the nth term of the series 11+12+14+21+22+24+31+32+34+… Then, Tn=n1+n2+n4=n1+n22−n2=nn2+n+1n2−n+1=121n2−n+1−1n2+n+1=1211+(n−1)n−11+n(n+1)∴ T1=1211−11+1⋅2T2=1211+1⋅2−11+2⋅3T3=1211+2⋅3−11+3⋅4⋯⋯ ⋯⋯⋯⋯Tn=1211+(n−1)n−11+n(n+1)On adding all these equations, we get ∑r=1n Tr=121−11+n(n+1)=n(n+1)2n2+n+1Similar Questions
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