Question

Find out first four terms 1x 3, 2x4, 3x5, 4x6​

Answer 1

Answer:

1x3+2x4+3x5+4x6+...+9999x10001+10000x10002

The nth term of this series can be written as;

T_n = n(n+2) = n^2+2n

If the sum of the series is S_n

S_n

= sum_(n=1)^10000n(n+2)

= sum_(n=1)^10000(2n)

= 1/6(2*10000^3+3*10000^2+10000)+1/2*10000*10001

= 3.334xx10^11

Therefore sum of the series is 3.334xx10^11

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