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2 years ago

Sum of n terms 1x2+2x3+3x4+4x5+...

Mathematics

1 answer:

lozanna [386]2 years ago

6 0

Answer:

1/3(n+1)³

Step-by-step explanation:

1x2+2x3+3x4+4x5+...= 1²+1+2²+2+3²+3+...+n²+n+1=

=(1²+2²+3²+...+n²)+(1+2+3+...+n+1)=

=1/6n(n+1)(2n+1)+1/2(n+1)(1+n+1)=

=1/6(n+1)(n(2n+1)+3(n+2))=

=1/6(n+1)(2n²+4n+2)=

=1/6(n+1)*2(n+1)²=

=1/3(n+1)³

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3 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

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Work out the size of one of the exterior angles

hodyreva [135]

Given Information :-

⠀

A polygon with 10 sides ( Decagon )

⠀

To Find :-

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The value of one of the exterior angles

⠀

Formula Used :-

⠀

$\qquad \diamond \: \underline{ \boxed{ \pink{ \sf Exterior ~angle = \dfrac {360^\circ}{no. ~of~sides}}}} \: \star$

⠀

Solution :-

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Putting the given values, we get,

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$\sf \dashrightarrow Exterior ~angle = \dfrac{360 ^\circ}{10} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \frac{36 \cancel{0}^\circ}{ \cancel{10}} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \underline{ \boxed{ \frak{ \red{36^\circ}}}} \: \star \\ \\$

Thus, the value of the exterior angles of a Decagon is 36°.

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$\underline{ \rule{227pt}{2pt}} \\ \\$

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2 years ago

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