Class 11

Math

Algebra

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 $aandb˙$

If $x=n=0∑∞ a_{n},y=n=0∑∞ b_{n},z=n=0∑∞ c_{n},wherera,b,andc$ 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 $1_{2}+(1_{2}+2_{2})+(1_{2}+2_{2}+3_{2})+$ 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,.......