Class 11

Math

Algebra

Sequences and Series

x and y are two +ve numbers suchs that xy =1. Then the minimum value of x + y is

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Find the sum $r=0∑n _{(n+r)}C_{r}$ .

Find the least value of $secA+secB+secC$ in an acute angled triangle.

If the sum of the series 2, 5, 8, 11, ... is 60100, then find the value of $n˙$

Let $S$ e the sum, $P$ the product, adn $R$ the sum of reciprocals of $n$ terms in a G.P. Prove that $P_{2}R_{n}=S_{n}˙$

The A.M. of two given positive numbers is 2. If the larger number is increased by 1, the G.M. of the numbers becomes equal to the A.M. of the given numbers. Then find the H.M.

Find the sum of the series $1×22 +2×35 ×2+3×410 ×2_{2}+4×517 ×2_{3}+→n$ terms.

Find the term of the series $25,2243 ,2021 ,1841 $ which is numerically the smallest.

A sequence of numbers $A_{∩}=1,2,3$ is defined as follows : $A_{1}=21 $ and for each $n≥2,$ $A_{n}=(2n2n−3 )A_{n−1}$ , then prove that $k=1∑n A_{k}<1,n≥1$