jee-main 2023 Q79

jee-main · India · session1_29jan_shift1 Arithmetic Sequences and Series Telescoping or Non-Standard Summation Involving an AP
Suppose f is a function satisfying $\mathrm { f } ( \mathrm { x } + \mathrm { y } ) = \mathrm { f } ( \mathrm { x } ) + \mathrm { f } ( \mathrm { y } )$ for all $\mathrm { x } , \mathrm { y } \in \mathbb { N }$ and $\mathrm { f } ( 1 ) = \frac { 1 } { 5 }$. If $\sum _ { n = 1 } ^ { m } \frac { f ( n ) } { n ( n + 1 ) ( n + 2 ) } = \frac { 1 } { 12 }$ then m is equal to $\_\_\_\_$ . 
Suppose f is a function satisfying $\mathrm { f } ( \mathrm { x } + \mathrm { y } ) = \mathrm { f } ( \mathrm { x } ) + \mathrm { f } ( \mathrm { y } )$ for all $\mathrm { x } , \mathrm { y } \in \mathbb { N }$ and $\mathrm { f } ( 1 ) = \frac { 1 } { 5 }$. If $\sum _ { n = 1 } ^ { m } \frac { f ( n ) } { n ( n + 1 ) ( n + 2 ) } = \frac { 1 } { 12 }$ then m is equal to $\_\_\_\_$ .
Paper Questions
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