Sequences and Series
Prove that [n+1/2]n>(n!)˙
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If A and G be A.M. and GM., respectively between two positive numbers, prove that the numbers are A±(A+G)(A−G).
For what value of x, the number −72,x,−72are in G.P.?
Find the sum to n terms of the series, whose nthterms is given by : n(n+1)(n+4)
Sum of the first p, q and r terms of an A.P are a, b and c, respectively.Prove that pa(q−r)+qb(r−p)+rc(p−q)=0
Find the sum of first n terms and the sum of first 5 terms of the geometric series 1 + 32+94+˙˙˙
Find the sum of first 24 terms of the list of numbers whose nth term is given by an=3+2n
Determine the AP whose 3rdterm is 5 and the 7thterm is 9.
Which term of the following sequences:(a) 2,22,4,. . . is 128? (b) 3,3,33,. . . is 729?(c) 31,91,271,. . . is 196831?