Sequences and Series
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If first three terms of the sequence 1/16,a,b,61 are in geometric series and last three terms are in harmonic series, then find the values of aandb˙
are in A.P. and ∣a∣<,∣b∣<1,and∣c∣<1,
then prove that x,yandz
are in H.P.
In a triangle ABC prove that a/(a+c)+b/(c+a)+c/(a+b)<2
Find the sum 12+(12+22)+(12+22+32)+
up to 22nd term.
Three non-zero numbers a,b,andc
are in A.P. Increasing a
by 1 or increasing c
by 2, the numbers are in G.P. Then find b˙
Find the sum to n
terms of the series 1/(1×2)+1/(2×3)+1/(3×4)++1/n(n+1)˙
The maximum sum of the series 20+1931+1832+⋯ is
13, 74, 290, 650,.......