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Formula
Sum of sequences
Answer
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$\sum_{ t = 1 }^{ 10 }{ t }$
$55$
Find the sum using the formula of a special sequence
$\sum_{ \color{#FF6800}{ t } = \color{#FF6800}{ 1 } }^{ \color{#FF6800}{ 10 } }{ \color{#FF6800}{ t } }$
$ $ Calculate the expression using $ \sum_{k=1}^{n}{k} = \dfrac{n\left(n+1\right)}{2}$
$\color{#FF6800}{ \dfrac { 10 \left ( 10 + 1 \right ) } { 2 } }$
$\dfrac { 10 \left ( \color{#FF6800}{ 10 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } \right ) } { 2 }$
$ $ Add $ 10 $ and $ 1$
$\dfrac { 10 \times \color{#FF6800}{ 11 } } { 2 }$
$\color{#FF6800}{ \dfrac { 10 \times 11 } { 2 } }$
$ $ Reduce the fraction $ $
$\color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 11 }$
$\color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 11 }$
$ $ Multiply $ 5 $ and $ 11$
$\color{#FF6800}{ 55 }$
$55$
Plug-in one by one
$\sum_{ \color{#FF6800}{ t } = \color{#FF6800}{ 1 } }^{ \color{#FF6800}{ 10 } }{ \color{#FF6800}{ t } }$
$ $ Plug-in one by one $ $
$\color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$\color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ + } \color{#FF6800}{ 6 } \color{#FF6800}{ + } \color{#FF6800}{ 7 } \color{#FF6800}{ + } \color{#FF6800}{ 8 } \color{#FF6800}{ + } \color{#FF6800}{ 9 } \color{#FF6800}{ + } \color{#FF6800}{ 10 }$
$ $ Calculate the value $ $
$\color{#FF6800}{ 55 }$
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