13b38+571ŕ¤°ŕ¤šnn+l

1.	13b38+571ŕ¤°ŕ¤šnn+l
Answer» Let k be ANY value of n Let Pk be proposition that 1 / ( 1•3) + 1 / (3•5) + 1 / (5•7) -----1 / [ (2k - 1)(2k + 1) ] = k / ( 2k + 1 ) Have to show that P1 is true and P ( k + 1 ) is true Consider P1--------------------LHS = 1/3RHS = 1/3Thus P1 is true Consider P ( k + 1 )-----------------------------LHS1/( 1•3) + 1/(3•5) + 1/(5•7) ----------1 / [ ( 2k + 1 ) ( 2k + 3 ) ] RHSk / ( 2k + 1 ) + 1 / [ ( 2k + 1 ) ( 2k + 3 ) ] Have to show that P ( k + 1 ) is true :- 2k^2 + 3 k + 1------------------------------------( 2 k + 3 ) ( 2 k + 1 ) ( 2k + 1 ) ( k + 1 )----------------------------( 2 k + 3 ) ( 2 k + 1 ) k + 1-----------2 k + 3 P1 is true and P (k + 1 ) is trueThus true for all kThus P n is true like my answer if you find it useful! thnxx😚😘😘😘 thnxx 😘😘😘

Answer»

Let k be ANY value of n

Let Pk be proposition that

1 / ( 1•3) + 1 / (3•5) + 1 / (5•7) -----1 / [ (2k - 1)(2k + 1) ] = k / ( 2k + 1 )

Have to show that P1 is true and P ( k + 1 ) is true

Consider P1--------------------LHS = 1/3RHS = 1/3Thus P1 is true

Consider P ( k + 1 )-----------------------------LHS1/( 1•3) + 1/(3•5) + 1/(5•7) ----------1 / [ ( 2k + 1 ) ( 2k + 3 ) ]

RHSk / ( 2k + 1 ) + 1 / [ ( 2k + 1 ) ( 2k + 3 ) ]

Have to show that P ( k + 1 ) is true :-

2k^2 + 3 k + 1------------------------------------( 2 k + 3 ) ( 2 k + 1 )

( 2k + 1 ) ( k + 1 )----------------------------( 2 k + 3 ) ( 2 k + 1 )

k + 1-----------2 k + 3

P1 is true and P (k + 1 ) is trueThus true for all kThus P n is true

like my answer if you find it useful!

thnxx😚😘😘😘

thnxx 😘😘😘

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