If `a_1,a_2,a_3, ,a_n` are an A.P. of non-zero terms, prove that `1/(a_1a_2)+1/(a_2a_3)++1/(a_(n...

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If a_1, a_2, a_3, ……, a_n be an A.P. of non-zero terms, prove that : 1/a_1 a_2+1/a_2 a_3+………... If a_1, a_2, a_3, ……, a_n be an A.P. of non-zero terms, prove that : 1/a_1 a_2+1/a_2 a_3+………...
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if a1,a2, a3 ,.... an are in A.P., where ai ( greater then zero ) for all i, show that ... ||#series if a1,a2, a3 ,.... an are in A.P., where ai ( greater then zero ) for all i, show that ... ||#series
If `a_1, a_2, a_3,.....a_n` are in H.P. and `a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 If `a_1, a_2, a_3,.....a_n` are in H.P. and `a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1
If `a_1,a_2,a_3,...,a_(n+1)` are in A.P. , then `1/(a_1a_2)+1/(a_2a_3)....+1/(a_na_(n+1))` is If `a_1,a_2,a_3,...,a_(n+1)` are in A.P. , then `1/(a_1a_2)+1/(a_2a_3)....+1/(a_na_(n+1))` is
prove that ((1+a1+a1^2 )(1+a2+a2^2 )(1+a3+a3^2 )…⋅(1+an+an^2 ))/(a1⋅a2⋅a3..…an )≥ 3^n prove that ((1+a1+a1^2 )(1+a2+a2^2 )(1+a3+a3^2 )…⋅(1+an+an^2 ))/(a1⋅a2⋅a3..…an )≥ 3^n
Let \[{a_n}\] be the nth term of an A.P. If \[{S_n} = {a_1} + {a_2} + {a_3} + ..... + {a_n} = 700 Let \[{a_n}\] be the nth term of an A.P. If \[{S_n} = {a_1} + {a_2} + {a_3} + ..... + {a_n} = 700