Sequences and Series
If a2+b2+c2=2,x2+y2+z2=2, where a,b,c,x,y,z>0, then maximum value of ax + by + cz is
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If a, b, c, d and p are different real numbers such that (a2+b2+c2)p2−2(ab+bc+cd)p+(b2+c2+d2)≤0, then show that a, b, c and d are in G.P.
Which term of the G.P., 2, 8, 32, . . . up to n terms in 131072?
Find the sum of the following series up to n terms:(i) 5+55+555+.... (ii) .6+.66+.666+....
If a, b, c, d are in G.P., prove that (an+bn),(bn+cn),(cn+an)are in G.P.
For the following AP's, write the first term and the common difference:(i) 3,1,−1,−3,…(ii) −5,−1,3,7,…(iii) 31,35,39,311……(iv) 0.6,1.7,2.8,3.9,…
If a (b1+c1), b(c1+a1), c(a1+b1)
are in A.P. prove that a, b, c
are in A.P.
In a GP the 3rd term is 24 and the 6th term is 192. Find the 10th term.
Show that 12×2+22×3++˙˙˙n2×(n+1)1×22+2×32++˙˙˙n×(n+1)2=3n+13n+5˙