Sequences and Series
If A=cos2x+cos2x1,B=cosx−cosx1 ∀x=(2n±1)2π, then the minimum value of BA is
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are A.M.s between 2 and 12, then find the sum a+b+c+d+e+f˙
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 positive, then prove that a/(b+c)+b/(c+a)+c/(a+b)≥3/2.
Divide 32 into four parts which are in A.P. such that the ratio of the product of extremes to the product of means is 7:15.
Find the sum 212−2232+2352−2472+∞˙
Prove that [n+1/2]n>(n!)˙
are in G.P., then prove that (a3+b3)−1,(b3+c3)−1,(c3+d3)−1
are also in G.P.
Find the sum of the series 1×22+2×35×2+3×410×22+4×517×23+→n terms.